From 7bc3414ce00c1613150d08e2e7dc5dc7a24aaab1 Mon Sep 17 00:00:00 2001
From: GinoGiotto <73717712+GinoGiotto@users.noreply.github.com>
Date: Thu, 28 Mar 2024 02:16:10 +0100
Subject: [PATCH 1/4] discourage usage of theorems relying on ax-13

---
 set.mm | 770 +++++++++++++++++++++++++++++++++------------------------
 1 file changed, 448 insertions(+), 322 deletions(-)

diff --git a/set.mm b/set.mm
index 044a82e9e8..62e7d70489 100644
--- a/set.mm
+++ b/set.mm
@@ -20577,7 +20577,7 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
        theorem would have been a direct consequence of ~ ax-5 .  So essentially
        this theorem states, that a distinct variable condition can be replaced
        with an inequality between set variables.  (Contributed by NM,
-       30-Jun-2016.) $)
+       30-Jun-2016.)  (New usage is discouraged.) $)
     ax13v $p |- ( -. x = y -> ( y = z -> A. x y = z ) ) $=
       ( ax-13 ) ABCD $.
   $}
@@ -20599,8 +20599,8 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
     $( Derive ~ ax-13 from ~ ax13v and Tarski's FOL. This shows that the
        weakening in ~ ax13v is still sufficient for a complete system.
        (Contributed by NM, 21-Dec-2015.)  (Proof shortened by Wolf Lammen,
-       31-Jan-2018.)  Reduce axiom usage (Revised by Wolf Lammen,
-       2-Jun-2021.) $)
+       31-Jan-2018.)  Reduce axiom usage (Revised by Wolf Lammen, 2-Jun-2021.)
+       (New usage is discouraged.) $)
     ax13 $p |- ( -. x = y -> ( y = z -> A. x y = z ) ) $=
       ( vw weq wn wal wi wa wex equvinv ax13lem1 imp ax7v1 alanimi an4s exlimdv
       syl2an ex syl5bi ax13b mpbir ) ABEFZBCEZUDAGZHZHUCACEFZUFHHUCUGUFUDDBEZDC
@@ -20624,7 +20624,7 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
     $d x z $.
     $( An equation between setvar is free of any other setvar.  (Contributed by
        Wolf Lammen, 9-Jun-2019.)  Remove dependency on ~ ax-12 .  (Revised by
-       Wolf Lammen, 16-Dec-2022.) $)
+       Wolf Lammen, 16-Dec-2022.)  (New usage is discouraged.) $)
     nfeqf2 $p |- ( -. A. x x = y -> F/ x z = y ) $=
       ( weq wal wex wnf exnal hbe1 ax13lem2 ax13lem1 syldc eximdh hbe1a syl6com
       wn nfd sylbir ) ABDZAEPSPZAFZCBDZAGSAHUAUBAUBAFZUAUBAEZAFUDUCTUDAUBAITUCU
@@ -20635,7 +20635,8 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
     $d x z $.
     $( Quantifier introduction when one pair of variables is distinct.
        (Contributed by NM, 2-Jan-2002.)  (Revised by NM, 20-Jul-2015.)  Remove
-       dependency on ~ ax-11 .  (Revised by Wolf Lammen, 8-Sep-2018.) $)
+       dependency on ~ ax-11 .  (Revised by Wolf Lammen, 8-Sep-2018.)
+       (New usage is discouraged.) $)
     dveeq2 $p |- ( -. A. x x = y -> ( z = y -> A. x z = y ) ) $=
       ( weq wal wn nfeqf2 nf5rd ) ABDAEFCBDAABCGH $.
   $}
@@ -20643,7 +20644,7 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
   ${
     $d x z $.
     $( An equation between setvar is free of any other setvar.  (Contributed by
-       Wolf Lammen, 10-Jun-2019.) $)
+       Wolf Lammen, 10-Jun-2019.)  (New usage is discouraged.) $)
     nfeqf1 $p |- ( -. A. x x = y -> F/ x y = z ) $=
       ( weq wal wn wnf nfeqf2 equcom nfbii sylib ) ABDAEFCBDZAGBCDZAGABCHLMACBI
       JK $.
@@ -20653,7 +20654,7 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
     $d x z $.
     $( Quantifier introduction when one pair of variables is distinct.
        (Contributed by NM, 2-Jan-2002.)  Remove dependency on ~ ax-11 .
-       (Revised by Wolf Lammen, 8-Sep-2018.) $)
+       (Revised by Wolf Lammen, 8-Sep-2018.)  (New usage is discouraged.) $)
     dveeq1 $p |- ( -. A. x x = y -> ( y = z -> A. x y = z ) ) $=
       ( weq wal wn nfeqf1 nf5rd ) ABDAEFBCDAABCGH $.
   $}
@@ -20663,7 +20664,7 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
     $( A variable is effectively not free in an equality if it is not either of
        the involved variables. ` F/ ` version of ~ ax-c9 .  (Contributed by
        Mario Carneiro, 6-Oct-2016.)  Remove dependency on ~ ax-11 .  (Revised
-       by Wolf Lammen, 6-Sep-2018.) $)
+       by Wolf Lammen, 6-Sep-2018.)  (New usage is discouraged.) $)
     nfeqf $p |- ( ( -. A. z z = x /\ -. A. z z = y ) -> F/ z x = y ) $=
       ( vw weq wal wn wa nfna1 nfan wex equvinva dveeq1 imp equtr2 alanimi an4s
       syl2an ex exlimdv syl5 nf5d ) CAEZCFGZCBEZCFGZHZABEZCUDUFCUCCIUECIJUHADEZ
@@ -20673,7 +20674,7 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
 
   $( Derive set.mm's original ~ ax-c9 from the shorter ~ ax-13 .  (Contributed
      by NM, 29-Nov-2015.)  (Revised by NM, 24-Dec-2015.)  (Proof shortened by
-     Wolf Lammen, 29-Apr-2018.) $)
+     Wolf Lammen, 29-Apr-2018.)  (New usage is discouraged.) $)
   axc9 $p |- ( -. A. z z = x -> ( -. A. z z = y
               -> ( x = y -> A. z x = y ) ) ) $=
     ( weq wal wn wi wa nfeqf nf5rd ex ) CADCEFZCBDCEFZABDZNCEGLMHNCABCIJK $.
@@ -20689,7 +20690,7 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
 
        It is preferred to use ~ ax6ev when it is sufficient.  (Contributed by
        NM, 14-May-1993.)  Shortened after ~ ax13lem1 became available.
-       (Revised by Wolf Lammen, 8-Sep-2018.) $)
+       (Revised by Wolf Lammen, 8-Sep-2018.)  (New usage is discouraged.) $)
     ax6e $p |- E. x x = y $=
       ( vw weq wex 19.8a wn wi wal ax13lem1 ax6ev equtr eximii syl6com exlimiiv
       19.35i pm2.61i ) ABDZRAEZRAFCBDZRGZSHCUATTAISABCJTRAACDTRHAACKACBLMPNCBKO
@@ -20705,7 +20706,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
      can be traced back to ~ ax6v .  When possible, use the weaker ~ ax6v
      rather than ~ ax6 since the ~ ax6v derivation is much shorter and requires
      fewer axioms.  (Contributed by NM, 12-Nov-2013.)  (Revised by NM,
-     25-Jul-2015.)  (Proof shortened by Wolf Lammen, 4-Feb-2018.) $)
+     25-Jul-2015.)  (Proof shortened by Wolf Lammen, 4-Feb-2018.)
+     (New usage is discouraged.) $)
   ax6 $p |- -. A. x -. x = y $=
     ( weq wex wn wal ax6e df-ex mpbi ) ABCZADJEAFEABGJAHI $.
 
@@ -20715,14 +20717,15 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
 
      Normally, ~ axc10 should be used rather than ~ ax-c10 , except by theorems
      specifically studying the latter's properties.  (Contributed by NM,
-     5-Aug-1993.)  (Proof modification is discouraged.) $)
+     5-Aug-1993.)  (Proof modification is discouraged.)
+     (New usage is discouraged.) $)
   axc10 $p |- ( A. x ( x = y -> A. x ph ) -> ph ) $=
     ( weq wal wi wn ax6 con3 al2imi mtoi axc7 syl ) BCDZABEZFZBEZOGZBEZGAQSNGZB
     EBCHPRTBNOIJKABLM $.
 
   $( Closed theorem form of ~ spim .  (Contributed by NM, 15-Jan-2008.)
      (Revised by Mario Carneiro, 17-Oct-2016.)  (Proof shortened by Wolf
-     Lammen, 21-Mar-2023.) $)
+     Lammen, 21-Mar-2023.)  (New usage is discouraged.) $)
   spimt $p |- ( ( F/ x ps /\ A. x ( x = y -> ( ph -> ps ) ) ) ->
                                                          ( A. x ph -> ps ) ) $=
     ( weq wi wal wex wnf ax6e exim mpi 19.35 sylib id 19.9d sylan9r ) CDEZABFZF
@@ -20735,7 +20738,7 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
        [Tarski] p. 70.  The ~ spim series of theorems requires that only one
        direction of the substitution hypothesis hold.  (Contributed by NM,
        10-Jan-1993.)  (Revised by Mario Carneiro, 3-Oct-2016.)  (Proof
-       shortened by Wolf Lammen, 18-Feb-2018.) $)
+       shortened by Wolf Lammen, 18-Feb-2018.)  (New usage is discouraged.) $)
     spim $p |- ( A. x ph -> ps ) $=
       ( weq wi ax6e eximii 19.36i ) ABCECDGABHCCDIFJK $.
   $}
@@ -20745,7 +20748,7 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     spimed.2 $e |- ( x = y -> ( ph -> ps ) ) $.
     $( Deduction version of ~ spime .  See also ~ spimedv .  (Contributed by
        NM, 14-May-1993.)  (Revised by Mario Carneiro, 3-Oct-2016.)  (Proof
-       shortened by Wolf Lammen, 19-Feb-2018.) $)
+       shortened by Wolf Lammen, 19-Feb-2018.)  (New usage is discouraged.) $)
     spimed $p |- ( ch -> ( ph -> E. x ps ) ) $=
       ( wal wex nf5rd weq wi ax6e eximii 19.35i syl6 ) CAADHBDICADFJABDDEKABLDD
       EMGNOP $.
@@ -20756,7 +20759,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     spime.2 $e |- ( x = y -> ( ph -> ps ) ) $.
     $( Existential introduction, using implicit substitution.  Compare Lemma 14
        of [Tarski] p. 70.  (Contributed by NM, 7-Aug-1994.)  (Revised by Mario
-       Carneiro, 3-Oct-2016.)  (Proof shortened by Wolf Lammen, 6-Mar-2018.) $)
+       Carneiro, 3-Oct-2016.)  (Proof shortened by Wolf Lammen, 6-Mar-2018.)
+       (New usage is discouraged.) $)
     spime $p |- ( ph -> E. x ps ) $=
       ( wex wi wtru wnf a1i spimed mptru ) ABCGHABICDACJIEKFLM $.
   $}
@@ -20766,7 +20770,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     spimv.1 $e |- ( x = y -> ( ph -> ps ) ) $.
     $( A version of ~ spim with a distinct variable requirement instead of a
        bound-variable hypothesis.  See ~ spimfv and ~ spimvw for versions
-       requiring fewer axioms.  (Contributed by NM, 31-Jul-1993.) $)
+       requiring fewer axioms.  (Contributed by NM, 31-Jul-1993.)
+       (New usage is discouraged.) $)
     spimv $p |- ( A. x ph -> ps ) $=
       ( nfv spim ) ABCDBCFEG $.
 
@@ -20784,7 +20789,7 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     $d x ph $.
     spimev.1 $e |- ( x = y -> ( ph -> ps ) ) $.
     $( Distinct-variable version of ~ spime .  (Contributed by NM,
-       10-Jan-1993.) $)
+       10-Jan-1993.)  (New usage is discouraged.) $)
     spimev $p |- ( ph -> E. x ps ) $=
       ( nfv spime ) ABCDACFEG $.
   $}
@@ -20793,7 +20798,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     $d x ps $.
     spv.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Specialization, using implicit substitution.  See ~ spvv for a version
-       using fewer axioms.  (Contributed by NM, 30-Aug-1993.) $)
+       using fewer axioms.  (Contributed by NM, 30-Aug-1993.)
+       (New usage is discouraged.) $)
     spv $p |- ( A. x ph -> ps ) $=
       ( weq biimpd spimv ) ABCDCDFABEGH $.
   $}
@@ -20803,7 +20809,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     spei.2 $e |- ps $.
     $( Inference from existential specialization, using implicit substitution.
        Remove a distinct variable constraint.  (Contributed by NM,
-       19-Aug-1993.)  (Proof shortened by Wolf Lammen, 12-May-2018.) $)
+       19-Aug-1993.)  (Proof shortened by Wolf Lammen, 12-May-2018.)
+       (New usage is discouraged.) $)
     spei $p |- E. x ph $=
       ( weq ax6e mpbiri eximii ) CDGZACCDHKABFEIJ $.
   $}
@@ -20813,8 +20820,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     chvar.2 $e |- ( x = y -> ( ph <-> ps ) ) $.
     chvar.3 $e |- ph $.
     $( Implicit substitution of ` y ` for ` x ` into a theorem.  (Contributed
-       by Raph Levien, 9-Jul-2003.)  (Revised by Mario Carneiro,
-       3-Oct-2016.) $)
+       by Raph Levien, 9-Jul-2003.)  (Revised by Mario Carneiro, 3-Oct-2016.)
+       (New usage is discouraged.) $)
     chvar $p |- ps $=
       ( weq biimpd spim mpg ) ABCABCDECDHABFIJGK $.
   $}
@@ -20824,7 +20831,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     chvarv.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
     chvarv.2 $e |- ph $.
     $( Implicit substitution of ` y ` for ` x ` into a theorem.  (Contributed
-       by NM, 20-Apr-1994.)  (Proof shortened by Wolf Lammen, 22-Apr-2018.) $)
+       by NM, 20-Apr-1994.)  (Proof shortened by Wolf Lammen, 22-Apr-2018.)
+       (New usage is discouraged.) $)
     chvarv $p |- ps $=
       ( nfv chvar ) ABCDBCGEFH $.
   $}
@@ -20835,7 +20843,7 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbv3.3 $e |- ( x = y -> ( ph -> ps ) ) $.
     $( Rule used to change bound variables, using implicit substitution, that
        does not use ~ ax-c9 .  (Contributed by NM, 5-Aug-1993.)  (Proof
-       shortened by Wolf Lammen, 12-May-2018.) $)
+       shortened by Wolf Lammen, 12-May-2018.)  (New usage is discouraged.) $)
     cbv3 $p |- ( A. x ph -> A. y ps ) $=
       ( wal nf5ri hbal spim alrimih ) ACHBDADCADEIJABCDFGKL $.
   $}
@@ -20847,14 +20855,15 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     $( Rule used to change bound variables, using implicit substitution.  See
        ~ cbvalv , ~ cbvalv1 , and ~ cbvalvw for weaker versions.  The latter
        two use fewer axioms.  (Contributed by NM, 13-May-1993.)  (Revised by
-       Mario Carneiro, 3-Oct-2016.) $)
+       Mario Carneiro, 3-Oct-2016.)  (New usage is discouraged.) $)
     cbval $p |- ( A. x ph <-> A. y ps ) $=
       ( wal weq biimpd cbv3 wi biimprd equcoms impbii ) ACHBDHABCDEFCDIZABGJKBA
       DCFEBALCDPABGMNKO $.
 
     $( Rule used to change bound variables, using implicit substitution.  See
        ~ cbvexv , ~ cbvexv1 , and ~ cbvexvw for weaker versions.  The latter
-       two use fewer axioms.  (Contributed by NM, 21-Jun-1993.) $)
+       two use fewer axioms.  (Contributed by NM, 21-Jun-1993.)
+       (New usage is discouraged.) $)
     cbvex $p |- ( E. x ph <-> E. y ps ) $=
       ( wex wn wal nfn weq notbid cbval alnex 3bitr3i con4bii ) ACHZBDHZAIZCJBI
       ZDJRISITUACDADEKBCFKCDLABGMNACOBDOPQ $.
@@ -20866,14 +20875,16 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     $( Rule used to change bound variables, using implicit substitution.  See
        ~ cbvalvw for a version requiring fewer axioms, to be preferred when
        sufficient.  (Contributed by NM, 5-Aug-1993.)  Remove dependency on
-       ~ ax-10 , shorten.  (Revised by Wolf Lammen, 11-Sep-2023.) $)
+       ~ ax-10 , shorten.  (Revised by Wolf Lammen, 11-Sep-2023.)
+       (New usage is discouraged.) $)
     cbvalv $p |- ( A. x ph <-> A. y ps ) $=
       ( nfv cbval ) ABCDADFBCFEG $.
 
     $( Rule used to change bound variables, using implicit substitution.  See
        ~ cbvexvw for a version requiring fewer axioms, to be preferred when
        sufficient.  (Contributed by NM, 21-Jun-1993.)  Remove dependency on
-       ~ ax-10 , shorten.  (Revised by Wolf Lammen, 11-Sep-2023.) $)
+       ~ ax-10 , shorten.  (Revised by Wolf Lammen, 11-Sep-2023.)
+       (New usage is discouraged.) $)
     cbvexv $p |- ( E. x ph <-> E. y ps ) $=
       ( nfv cbvex ) ABCDADFBCFEG $.
 
@@ -20904,7 +20915,7 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
        ~ cbv1v with disjoint variable conditions, not depending on ~ ax-13 .
        (Contributed by NM, 5-Aug-1993.)  (Revised by Mario Carneiro,
        3-Oct-2016.)  Format hypotheses to common style.  (Revised by Wolf
-       Lammen, 13-May-2018.) $)
+       Lammen, 13-May-2018.)  (New usage is discouraged.) $)
     cbv1 $p |- ( ph -> ( A. x ps -> A. y ch ) ) $=
       ( wal wi nfim1 weq com12 a2d cbv3 19.21 3imtr3i pm2.86i ) ABDKZCEKZABLZDK
       ACLZEKAUALAUBLUCUDDEABEGHMACDFIMDENZABCAUEBCLJOPQABDFRACEGRST $.
@@ -20920,7 +20931,7 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
        ~ cbv2w with disjoint variable conditions, not depending on ~ ax-13 .
        (Contributed by NM, 5-Aug-1993.)  (Revised by Mario Carneiro,
        3-Oct-2016.)  Format hypotheses to common style, avoid ~ ax-10 .
-       (Revised by Wolf Lammen, 10-Sep-2023.) $)
+       (Revised by Wolf Lammen, 10-Sep-2023.)  (New usage is discouraged.) $)
     cbv2 $p |- ( ph -> ( A. x ps <-> A. y ch ) ) $=
       ( wal weq wb wi biimp syl6 cbv1 equcomi biimpr syl56 impbid ) ABDKCEKABCD
       EFGHIADELZBCMZBCNJBCOPQACBEDGFIHEDLUBAUCCBNEDRJBCSTQUA $.
@@ -20933,7 +20944,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbv3h.3 $e |- ( x = y -> ( ph -> ps ) ) $.
     $( Rule used to change bound variables, using implicit substitution.
        (Contributed by NM, 8-Jun-1993.)  (Proof shortened by Andrew Salmon,
-       25-May-2011.)  (Proof shortened by Wolf Lammen, 12-May-2018.) $)
+       25-May-2011.)  (Proof shortened by Wolf Lammen, 12-May-2018.)
+       (New usage is discouraged.) $)
     cbv3h $p |- ( A. x ph -> A. y ps ) $=
       ( nf5i cbv3 ) ABCDADEHBCFHGI $.
   $}
@@ -20944,7 +20956,7 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbv1h.3 $e |- ( ph -> ( x = y -> ( ps -> ch ) ) ) $.
     $( Rule used to change bound variables, using implicit substitution.
        (Contributed by NM, 11-May-1993.)  (Proof shortened by Wolf Lammen,
-       13-May-2018.) $)
+       13-May-2018.)  (New usage is discouraged.) $)
     cbv1h $p |- ( A. x A. y ph -> ( A. x ps -> A. y ch ) ) $=
       ( wal nfa1 nfa2 wi 2sp syl nf5d weq cbv1 ) AEIZDIZBCDERDJZAEDKZSBEUASABBE
       ILADEMZFNOSCDTSACCDILUBGNOSADEPBCLLUBHNQ $.
@@ -20955,7 +20967,7 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbv2h.2 $e |- ( ph -> ( ch -> A. x ch ) ) $.
     cbv2h.3 $e |- ( ph -> ( x = y -> ( ps <-> ch ) ) ) $.
     $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 11-May-1993.) $)
+       (Contributed by NM, 11-May-1993.)  (New usage is discouraged.) $)
     cbv2h $p |- ( A. x A. y ph -> ( A. x ps <-> A. y ch ) ) $=
       ( wal weq wb wi biimp syl6 cbv1h equcomi biimpr syl56 alcoms impbid ) AEI
       DIBDIZCEIZABCDEFGADEJZBCKZBCLHBCMNOAUBUALEDACBEDGFEDJUCAUDCBLEDPHBCQROST
@@ -20986,14 +20998,15 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
        particularly useful in conjunction with ~ dvelim .  See ~ cbvaldw for a
        version with ` x , y ` disjoint, not depending on ~ ax-13 .
        (Contributed by NM, 2-Jan-2002.)  (Revised by Mario Carneiro,
-       6-Oct-2016.)  (Revised by Wolf Lammen, 13-May-2018.) $)
+       6-Oct-2016.)  (Revised by Wolf Lammen, 13-May-2018.)
+       (New usage is discouraged.) $)
     cbvald $p |- ( ph -> ( A. x ps <-> A. y ch ) ) $=
       ( nfv nfvd cbv2 ) ABCDEADIFGACDJHK $.
 
     $( Deduction used to change bound variables, using implicit substitution,
        particularly useful in conjunction with ~ dvelim .  See also ~ cbvexdw .
        (Contributed by NM, 2-Jan-2002.)  (Revised by Mario Carneiro,
-       6-Oct-2016.) $)
+       6-Oct-2016.)  (New usage is discouraged.) $)
     cbvexd $p |- ( ph -> ( E. x ps <-> E. y ch ) ) $=
       ( wex wn wal nfnd weq wb notbi syl6ib cbvald alnex 3bitr3g con4bid ) ABDI
       ZCEIZABJZDKCJZEKUAJUBJAUCUDDEFABEGLADEMBCNUCUDNHBCOPQBDRCERST $.
@@ -21004,13 +21017,15 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbvaldva.1 $e |- ( ( ph /\ x = y ) -> ( ps <-> ch ) ) $.
     $( Rule used to change the bound variable in a universal quantifier with
        implicit substitution.  Deduction form.  See also ~ cbvaldvaw .
-       (Contributed by David Moews, 1-May-2017.) $)
+       (Contributed by David Moews, 1-May-2017.)
+       (New usage is discouraged.) $)
     cbvaldva $p |- ( ph -> ( A. x ps <-> A. y ch ) ) $=
       ( nfv nfvd weq wb ex cbvald ) ABCDEAEGABEHADEIBCJFKL $.
 
     $( Rule used to change the bound variable in an existential quantifier with
        implicit substitution.  Deduction form.  See also ~ cbvexdvaw .
-       (Contributed by David Moews, 1-May-2017.) $)
+       (Contributed by David Moews, 1-May-2017.)
+       (New usage is discouraged.) $)
     cbvexdva $p |- ( ph -> ( E. x ps <-> E. y ch ) ) $=
       ( nfv nfvd weq wb ex cbvexd ) ABCDEAEGABEHADEIBCJFKL $.
   $}
@@ -21024,7 +21039,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbval2.5 $e |- ( ( x = z /\ y = w ) -> ( ph <-> ps ) ) $.
     $( Rule used to change bound variables, using implicit substitution.
        (Contributed by NM, 22-Dec-2003.)  (Revised by Mario Carneiro,
-       6-Oct-2016.)  (Proof shortened by Wolf Lammen, 11-Sep-2023.) $)
+       6-Oct-2016.)  (Proof shortened by Wolf Lammen, 11-Sep-2023.)
+       (New usage is discouraged.) $)
     cbval2 $p |- ( A. x A. y ph <-> A. z A. w ps ) $=
       ( wal nfal weq nfv wnf a1i wb ex cbv2 cbval ) ADLBFLCEAEDGMBCFIMCENZABDFU
       BDOUBFOAFPUBHQBDPUBJQUBDFNABRKSTUA $.
@@ -21040,7 +21056,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
 
     $( Rule used to change bound variables, using implicit substitution.
        (Contributed by NM, 14-Sep-2003.)  (Revised by Mario Carneiro,
-       6-Oct-2016.)  (Proof shortened by Wolf Lammen, 16-Jun-2019.) $)
+       6-Oct-2016.)  (Proof shortened by Wolf Lammen, 16-Jun-2019.)
+       (New usage is discouraged.) $)
     cbvex2 $p |- ( E. x E. y ph <-> E. z E. w ps ) $=
       ( wex wn wal nfn weq wa notbid cbval2 2nexaln 3bitr4i con4bii ) ADLCLZBFL
       ELZAMZDNCNBMZFNENUCMUDMUEUFCDEFAEGOAFHOBCIOBDJOCEPDFPQABKRSACDTBEFTUAUB
@@ -21052,13 +21069,13 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbval2vv.1 $e |- ( ( x = z /\ y = w ) -> ( ph <-> ps ) ) $.
     $( Rule used to change bound variables, using implicit substitution.
        (Contributed by NM, 4-Feb-2005.)  Remove dependency on ~ ax-10 .
-       (Revised by Wolf Lammen, 18-Jul-2021.) $)
+       (Revised by Wolf Lammen, 18-Jul-2021.)  (New usage is discouraged.) $)
     cbval2vv $p |- ( A. x A. y ph <-> A. z A. w ps ) $=
       ( wal weq cbvaldva cbvalv ) ADHBFHCECEIABDFGJK $.
 
     $( Rule used to change bound variables, using implicit substitution.
        (Contributed by NM, 26-Jul-1995.)  Remove dependency on ~ ax-10 .
-       (Revised by Wolf Lammen, 18-Jul-2021.) $)
+       (Revised by Wolf Lammen, 18-Jul-2021.)  (New usage is discouraged.) $)
     cbvex2vv $p |- ( E. x E. y ph <-> E. z E. w ps ) $=
       ( wex weq cbvexdva cbvexv ) ADHBFHCECEIABDFGJK $.
   $}
@@ -21074,7 +21091,7 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbvex4v.1 $e |- ( ( x = v /\ y = u ) -> ( ph <-> ps ) ) $.
     cbvex4v.2 $e |- ( ( z = f /\ w = g ) -> ( ps <-> ch ) ) $.
     $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 26-Jul-1995.) $)
+       (Contributed by NM, 26-Jul-1995.)  (New usage is discouraged.) $)
     cbvex4v $p |- ( E. x E. y E. z E. w ph <-> E. v E. u E. f E. g ch ) $=
       ( wex weq wa 2exbidv cbvex2vv 2exbii bitri ) AGNFNZENDNBGNFNZINHNCKNJNZIN
       HNUAUBDEHIDHOEIOPABFGLQRUBUCHIBCFGJKMRST $.
@@ -21084,7 +21101,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
      requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
      hypothesis ( ~ equs45f ).  See ~ equs4v for a version requiring fewer
      axioms.  (Contributed by NM, 10-May-1993.)  (Proof shortened by Mario
-     Carneiro, 20-May-2014.)  (Proof shortened by Wolf Lammen, 5-Feb-2018.) $)
+     Carneiro, 20-May-2014.)  (Proof shortened by Wolf Lammen, 5-Feb-2018.)
+     (New usage is discouraged.) $)
   equs4 $p |- ( A. x ( x = y -> ph ) -> E. x ( x = y /\ ph ) ) $=
     ( weq wi wal wex wa ax6e exintr mpi ) BCDZAEBFLBGLAHBGBCILABJK $.
 
@@ -21096,7 +21114,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
        fewer axioms.  See also the dual form ~ equsex .  (Contributed by NM,
        2-Jun-1993.)  (Proof shortened by Andrew Salmon, 12-Aug-2011.)  (Revised
        by Mario Carneiro, 3-Oct-2016.)  (Proof shortened by Wolf Lammen,
-       5-Feb-2018.) $)
+       5-Feb-2018.)  (New usage is discouraged.) $)
     equsal $p |- ( A. x ( x = y -> ph ) <-> ps ) $=
       ( weq wi wal wex 19.23 pm5.74i albii ax6e a1bi 3bitr4i ) CDGZBHZCIQCJZBHQ
       AHZCIBQBCEKTRCQABFLMSBCDNOP $.
@@ -21105,7 +21123,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
        ~ equsexv for versions with disjoint variable conditions proved from
        fewer axioms.  See also the dual form ~ equsal .  See ~ equsexALT for an
        alternate proof.  (Contributed by NM, 5-Aug-1993.)  (Revised by Mario
-       Carneiro, 3-Oct-2016.)  (Proof shortened by Wolf Lammen, 6-Feb-2018.) $)
+       Carneiro, 3-Oct-2016.)  (Proof shortened by Wolf Lammen, 6-Feb-2018.)
+       (New usage is discouraged.) $)
     equsex $p |- ( E. x ( x = y /\ ph ) <-> ps ) $=
       ( weq wa wex biimpa exlimi wi wal equsal equs4 sylbir impbii ) CDGZAHZCIZ
       BSBCERABFJKBRALCMTABCDEFNACDOPQ $.
@@ -21128,13 +21147,14 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     equsalh.2 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( An equivalence related to implicit substitution.  See ~ equsalhw for a
        version with a disjoint variable condition requiring fewer axioms.
-       (Contributed by NM, 2-Jun-1993.) $)
+       (Contributed by NM, 2-Jun-1993.)  (New usage is discouraged.) $)
     equsalh $p |- ( A. x ( x = y -> ph ) <-> ps ) $=
       ( nf5i equsal ) ABCDBCEGFH $.
 
     $( An equivalence related to implicit substitution.  See ~ equsexhv for a
        version with a disjoint variable condition which does not require
-       ~ ax-13 .  (Contributed by NM, 5-Aug-1993.) $)
+       ~ ax-13 .  (Contributed by NM, 5-Aug-1993.)
+       (New usage is discouraged.) $)
     equsexh $p |- ( E. x ( x = y /\ ph ) <-> ps ) $=
       ( nf5i equsex ) ABCDBCEGFH $.
   $}
@@ -21148,7 +21168,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
        Normally, ~ axc15 should be used rather than ~ ax-c15 , except by
        theorems specifically studying the latter's properties.  (Contributed by
-       NM, 2-Feb-2007.)  (Proof shortened by Wolf Lammen, 26-Mar-2023.) $)
+       NM, 2-Feb-2007.)  (Proof shortened by Wolf Lammen, 26-Mar-2023.)
+       (New usage is discouraged.) $)
     axc15 $p |- ( -. A. x x = y ->
                  ( x = y -> ( ph -> A. x ( x = y -> ph ) ) ) ) $=
       ( vz weq wal wn wex ax6ev dveeq2 ax12v equeuclr sps imim1d al2imi imim12d
@@ -21170,12 +21191,14 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   $( Rederivation of axiom ~ ax-12 from ~ ax12v (used only via ~ sp ) ,
      ~ axc11r , and ~ axc15 (on top of Tarski's FOL).  (Contributed by NM,
      22-Jan-2007.)  Proof uses contemporary axioms.  (Revised by Wolf Lammen,
-     8-Aug-2020.)  (Proof shortened by BJ, 4-Jul-2021.) $)
+     8-Aug-2020.)  (Proof shortened by BJ, 4-Jul-2021.)
+     (New usage is discouraged.) $)
   ax12 $p |- ( x = y -> ( A. y ph -> A. x ( x = y -> ph ) ) ) $=
     ( weq wal wi axc11r ala1 syl6 a1d wn sp axc15 syl7 pm2.61i ) BCDZBEZPACEZPA
     FBEZFZFQTPQRABESACBGAPBHIJRAQKPSACLABCMNO $.
 
-  $( A bidirectional version of ~ axc15 .  (Contributed by NM, 30-Jun-2006.) $)
+  $( A bidirectional version of ~ axc15 .  (Contributed by NM, 30-Jun-2006.)
+     (New usage is discouraged.) $)
   ax12b $p |- ( ( -. A. x x = y /\ x = y ) ->
               ( ph <-> A. x ( x = y -> ph ) ) ) $=
     ( weq wal wn wa wi axc15 imp sp com12 adantl impbid ) BCDZBEFZOGAOAHZBEZPOA
@@ -21199,7 +21222,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
        (Contributed by NM, 10-May-1993.)  (Revised by NM, 7-Nov-2015.)  (Proof
        shortened by Wolf Lammen, 6-Mar-2018.)  (Revised by Wolf Lammen,
        30-Nov-2019.)  (Proof shortened by BJ, 29-Mar-2021.)  (Proof shortened
-       by Wolf Lammen, 2-Jul-2021.) $)
+       by Wolf Lammen, 2-Jul-2021.)  (New usage is discouraged.) $)
     axc11n $p |- ( A. x x = y -> A. y y = x ) $=
       ( vz weq wal wn dveeq1 com12 axc11r aev syl6 syl9 ax6evr exlimiiv pm2.18d
       wi ) ABDAEZBADBEZACDZQRFZRPPCSTSBEZQRTSUABACGHQUASAERSBAIACBABJKLCAMNO $.
@@ -21208,14 +21231,14 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   $( Commutation law for identical variable specifiers.  Both sides of the
      biconditional are true when ` x ` and ` y ` are substituted with the same
      variable.  (Contributed by NM, 10-May-1993.)  Change to a biconditional.
-     (Revised by BJ, 26-Sep-2019.) $)
+     (Revised by BJ, 26-Sep-2019.)  (New usage is discouraged.) $)
   aecom $p |- ( A. x x = y <-> A. y y = x ) $=
     ( weq wal axc11n impbii ) ABCADBACBDABEBAEF $.
 
   ${
     aecoms.1 $e |- ( A. x x = y -> ph ) $.
     $( A commutation rule for identical variable specifiers.  (Contributed by
-       NM, 10-May-1993.) $)
+       NM, 10-May-1993.)  (New usage is discouraged.) $)
     aecoms $p |- ( A. y y = x -> ph ) $=
       ( weq wal aecom sylbi ) CBECFBCEBFACBGDH $.
   $}
@@ -21223,7 +21246,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   ${
     naecoms.1 $e |- ( -. A. x x = y -> ph ) $.
     $( A commutation rule for distinct variable specifiers.  (Contributed by
-       NM, 2-Jan-2002.) $)
+       NM, 2-Jan-2002.)  (New usage is discouraged.) $)
     naecoms $p |- ( -. A. y y = x -> ph ) $=
       ( weq wal aecom sylnbir ) CBECFBCEBFABCGDH $.
   $}
@@ -21231,13 +21254,14 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   $( Show that ~ ax-c11 can be derived from ~ ax-c11n in the form of ~ axc11n .
      Normally, ~ axc11 should be used rather than ~ ax-c11 , except by theorems
      specifically studying the latter's properties.  (Contributed by NM,
-     16-May-2008.)  (Proof shortened by Wolf Lammen, 21-Apr-2018.) $)
+     16-May-2008.)  (Proof shortened by Wolf Lammen, 21-Apr-2018.)
+     (New usage is discouraged.) $)
   axc11 $p |- ( A. x x = y -> ( A. x ph -> A. y ph ) ) $=
     ( wal wi axc11r aecoms ) ABDACDECBABCFG $.
 
   $( All variables are effectively bound in an identical variable specifier.
      (Contributed by NM, 13-May-1993.)  (Proof shortened by Wolf Lammen,
-     21-Apr-2018.) $)
+     21-Apr-2018.)  (New usage is discouraged.) $)
   hbae $p |- ( A. x x = y -> A. z A. x x = y ) $=
     ( weq wal wi wn sp axc9 syl7 axc11r axc11 pm2.43i syl5 pm2.61ii axc4i ax-11
     syl ) ABDZAEZSCEZAETCESUAACADCEZCBDCEZTUAFTSUBGUCGUASAHABCIJSACKTSBEZUCUATU
@@ -21246,24 +21270,26 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   $( All variables are effectively bound in a distinct variable specifier.  A
      version with a distinct variable condition based on fewer axioms is
      ~ hbnaev .  Lemma L19 in [Megill] p. 446 (p. 14 of the preprint).
-     (Contributed by NM, 13-May-1993.) $)
+     (Contributed by NM, 13-May-1993.)  (New usage is discouraged.) $)
   hbnae $p |- ( -. A. x x = y -> A. z -. A. x x = y ) $=
     ( weq wal hbae hbn ) ABDAECABCFG $.
 
   $( All variables are effectively bound in an identical variable specifier.
-     (Contributed by Mario Carneiro, 11-Aug-2016.) $)
+     (Contributed by Mario Carneiro, 11-Aug-2016.)
+     (New usage is discouraged.) $)
   nfae $p |- F/ z A. x x = y $=
     ( weq wal hbae nf5i ) ABDAECABCFG $.
 
   $( All variables are effectively bound in a distinct variable specifier.  See
-     also ~ nfnaew .  (Contributed by Mario Carneiro, 11-Aug-2016.) $)
+     also ~ nfnaew .  (Contributed by Mario Carneiro, 11-Aug-2016.)
+     (New usage is discouraged.) $)
   nfnae $p |- F/ z -. A. x x = y $=
     ( weq wal nfae nfn ) ABDAECABCFG $.
 
   ${
     hbnaes.1 $e |- ( A. z -. A. x x = y -> ph ) $.
     $( Rule that applies ~ hbnae to antecedent.  (Contributed by NM,
-       15-May-1993.) $)
+       15-May-1993.)  (New usage is discouraged.) $)
     hbnaes $p |- ( -. A. x x = y -> ph ) $=
       ( weq wal wn hbnae syl ) BCFBGHZKDGABCDIEJ $.
   $}
@@ -21273,7 +21299,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     axc16i.1 $e |- ( x = z -> ( ph <-> ps ) ) $.
     axc16i.2 $e |- ( ps -> A. x ps ) $.
     $( Inference with ~ axc16 as its conclusion.  (Contributed by NM,
-       20-May-2008.)  (Proof modification is discouraged.) $)
+       20-May-2008.)  (Proof modification is discouraged.)
+       (New usage is discouraged.) $)
     axc16i $p |- ( A. x x = y -> ( ph -> A. x ph ) ) $=
       ( weq wal wi nfv ax7 cbv3 spimvw equcomi syl syl5com alimdv mpcom alimi
       biimpcd nf5i biimprd syl6com 3syl ) CDHZCIEDHZEIZCEHZEIZAACIZJUFUGCEUFEKU
@@ -21295,14 +21322,14 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
        Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).
        (Contributed by NM, 27-Feb-2005.)  Allow a shortening of ~ dral1 .
-       (Revised by Wolf Lammen, 4-Mar-2018.) $)
+       (Revised by Wolf Lammen, 4-Mar-2018.)  (New usage is discouraged.) $)
     dral2 $p |- ( A. x x = y -> ( A. z ph <-> A. z ps ) ) $=
       ( weq wal nfae albid ) CDGCHABECDEIFJ $.
 
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
        Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).
        (Contributed by NM, 24-Nov-1994.)  Remove dependency on ~ ax-11 .
-       (Revised by Wolf Lammen, 6-Sep-2018.) $)
+       (Revised by Wolf Lammen, 6-Sep-2018.)  (New usage is discouraged.) $)
     dral1 $p |- ( A. x x = y -> ( A. x ph <-> A. y ps ) ) $=
       ( weq wal nfa1 albid axc11 axc11r impbid bitrd ) CDFZCGZACGBCGZBDGZOABCNC
       HEIOPQBCDJBDCKLM $.
@@ -21317,26 +21344,27 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
        Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).
-       (Contributed by NM, 27-Feb-2005.) $)
+       (Contributed by NM, 27-Feb-2005.)  (New usage is discouraged.) $)
     drex1 $p |- ( A. x x = y -> ( E. x ph <-> E. y ps ) ) $=
       ( weq wal wn wex notbid dral1 df-ex 3bitr4g ) CDFCGZAHZCGZHBHZDGZHACIBDIN
       PROQCDNABEJKJACLBDLM $.
 
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
        Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).
-       (Contributed by NM, 27-Feb-2005.) $)
+       (Contributed by NM, 27-Feb-2005.)  (New usage is discouraged.) $)
     drex2 $p |- ( A. x x = y -> ( E. z ph <-> E. z ps ) ) $=
       ( weq wal nfae exbid ) CDGCHABECDEIFJ $.
 
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
-       (Contributed by Mario Carneiro, 4-Oct-2016.) $)
+       (Contributed by Mario Carneiro, 4-Oct-2016.)
+       (New usage is discouraged.) $)
     drnf1 $p |- ( A. x x = y -> ( F/ x ph <-> F/ y ps ) ) $=
       ( weq wal wi wnf dral1 imbi12d nf5 3bitr4g ) CDFCGZAACGZHZCGBBDGZHZDGACIB
       DIPRCDNABOQEABCDEJKJACLBDLM $.
 
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
        (Contributed by Mario Carneiro, 4-Oct-2016.)  (Proof shortened by Wolf
-       Lammen, 5-May-2018.) $)
+       Lammen, 5-May-2018.)  (New usage is discouraged.) $)
     drnf2 $p |- ( A. x x = y -> ( F/ z ph <-> F/ z ps ) ) $=
       ( weq wal nfae nfbidf ) CDGCHABECDEIFJ $.
   $}
@@ -21346,14 +21374,14 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     nfald2.2 $e |- ( ( ph /\ -. A. x x = y ) -> F/ x ps ) $.
     $( Variation on ~ nfald which adds the hypothesis that ` x ` and ` y ` are
        distinct in the inner subproof.  (Contributed by Mario Carneiro,
-       8-Oct-2016.) $)
+       8-Oct-2016.)  (New usage is discouraged.) $)
     nfald2 $p |- ( ph -> F/ x A. y ps ) $=
       ( weq wal wnf wn wa nfnae nfan nfald ex nfa1 biidd drnf1 mpbiri pm2.61d2
       ) ACDGCHZBDHZCIZAUAJZUCAUDKBCDAUDDECDDLMFNOUAUCUBDIBDPUBUBCDUAUBQRST $.
 
     $( Variation on ~ nfexd which adds the hypothesis that ` x ` and ` y ` are
        distinct in the inner subproof.  (Contributed by Mario Carneiro,
-       8-Oct-2016.) $)
+       8-Oct-2016.)  (New usage is discouraged.) $)
     nfexd2 $p |- ( ph -> F/ x E. y ps ) $=
       ( wex wn wal df-ex weq wa nfnd nfald2 nfxfrd ) BDGBHZDIZHACBDJAQCAPCDEACD
       KCIHLBCFMNMO $.
@@ -21365,7 +21393,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
        hypothesis saying that ` y ` is not free in ` ph ` , but ` x ` can be
        free in ` ph ` (and there is no distinct variable condition on ` x ` and
        ` y ` ).  (Contributed by Mario Carneiro, 20-Mar-2013.)  (Proof
-       shortened by Wolf Lammen, 14-May-2018.) $)
+       shortened by Wolf Lammen, 14-May-2018.)  (New usage is discouraged.) $)
     exdistrf $p |- ( E. x E. y ( ph /\ ps ) -> E. x ( ph /\ E. y ps ) ) $=
       ( wa wex weq wal wi 19.8a anim2i eximi biidd drex1 syl5ibr wn 19.40 19.9d
       nfe1 anim1d syl56 pm2.61i exlimi ) ABFZDGZABDGZFZCGZCUHCTCDHCIZUFUIJUFUIU
@@ -21379,7 +21407,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     dvelimf.3 $e |- ( z = y -> ( ph <-> ps ) ) $.
     $( Version of ~ dvelimv without any variable restrictions.  (Contributed by
        NM, 1-Oct-2002.)  (Revised by Mario Carneiro, 6-Oct-2016.)  (Proof
-       shortened by Wolf Lammen, 11-May-2018.) $)
+       shortened by Wolf Lammen, 11-May-2018.)  (New usage is discouraged.) $)
     dvelimf $p |- ( -. A. x x = y -> F/ x ps ) $=
       ( weq wi wal wn equsal bicomi nfnae wa wnf nfeqf ancoms a1i nfald2 nfxfrd
       nfimd ) BEDIZAJZEKZCDICKLZCUFBABEDGHMNUGUECECDEOUGCEICKLZPZUDACUHUGUDCQED
@@ -21394,7 +21422,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     dvelimdf.5 $e |- ( ph -> ( z = y -> ( ps <-> ch ) ) ) $.
     $( Deduction form of ~ dvelimf .  (Contributed by NM, 7-Apr-2004.)
        (Revised by Mario Carneiro, 6-Oct-2016.)  (Proof shortened by Wolf
-       Lammen, 11-May-2018.) $)
+       Lammen, 11-May-2018.)  (New usage is discouraged.) $)
     dvelimdf $p |- ( ph -> ( -. A. x x = y -> F/ x ch ) ) $=
       ( weq wal wn wi wnf nfim1 wb com12 pm5.74d dvelimf pm5.5 nfbidf syl5ib )
       DELDMNACOZDPACDPABOUEDEFABDGIQACFHJQFELZABCAUFBCRKSTUAAUECDGACUBUCUD $.
@@ -21405,7 +21433,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     dvelimh.2 $e |- ( ps -> A. z ps ) $.
     dvelimh.3 $e |- ( z = y -> ( ph <-> ps ) ) $.
     $( Version of ~ dvelim without any variable restrictions.  (Contributed by
-       NM, 1-Oct-2002.)  (Proof shortened by Wolf Lammen, 11-May-2018.) $)
+       NM, 1-Oct-2002.)  (Proof shortened by Wolf Lammen, 11-May-2018.)
+       (New usage is discouraged.) $)
     dvelimh $p |- ( -. A. x x = y -> ( ps -> A. x ps ) ) $=
       ( weq wal wn nf5i dvelimf nf5rd ) CDICJKBCABCDEACFLBEGLHMN $.
   $}
@@ -21427,7 +21456,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
        Other variants of this theorem are ~ dvelimh (with no distinct variable
        restrictions) and ~ dvelimhw (that avoids ~ ax-13 ).  (Contributed by
-       NM, 23-Nov-1994.) $)
+       NM, 23-Nov-1994.)  (New usage is discouraged.) $)
     dvelim $p |- ( -. A. x x = y -> ( ps -> A. x ps ) ) $=
       ( ax-5 dvelimh ) ABCDEFBEHGI $.
   $}
@@ -21437,7 +21466,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     dvelimv.1 $e |- ( z = y -> ( ph <-> ps ) ) $.
     $( Similar to ~ dvelim with first hypothesis replaced by a distinct
        variable condition.  (Contributed by NM, 25-Jul-2015.)  (Proof shortened
-       by Wolf Lammen, 30-Apr-2018.) $)
+       by Wolf Lammen, 30-Apr-2018.)  (New usage is discouraged.) $)
     dvelimv $p |- ( -. A. x x = y -> ( ps -> A. x ps ) ) $=
       ( ax-5 dvelim ) ABCDEACGFH $.
   $}
@@ -21447,7 +21476,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     dvelimnf.1 $e |- F/ x ph $.
     dvelimnf.2 $e |- ( z = y -> ( ph <-> ps ) ) $.
     $( Version of ~ dvelim using "not free" notation.  (Contributed by Mario
-       Carneiro, 9-Oct-2016.) $)
+       Carneiro, 9-Oct-2016.)  (New usage is discouraged.) $)
     dvelimnf $p |- ( -. A. x x = y -> F/ x ps ) $=
       ( nfv dvelimf ) ABCDEFBEHGI $.
   $}
@@ -21466,7 +21495,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
      ~ equvinv for a shorter proof requiring fewer axioms when ` z ` is
      required to be distinct from ` x ` and ` y ` .  (Contributed by NM,
      10-Jan-1993.)  (Proof shortened by Andrew Salmon, 25-May-2011.)  (Proof
-     shortened by Wolf Lammen, 16-Sep-2023.) $)
+     shortened by Wolf Lammen, 16-Sep-2023.)  (New usage is discouraged.) $)
   equvini $p |- ( x = y -> E. z ( x = z /\ z = y ) ) $=
     ( weq wa wex wi equtr equcomi jctild 19.8a syl6 wal ax13 ax6e eximii 19.35i
     wn pm2.61i ) CADZABDZACDZCBDZEZCFZGTUAUDUETUAUCUBCABHCAIJZUDCKLTRUAUACMUECA
@@ -21484,7 +21513,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   $( A variable elimination law for equality with no distinct variable
      requirements.  Compare ~ equvini .  (Contributed by NM, 1-Mar-2013.)
      (Proof shortened by Mario Carneiro, 17-Oct-2016.)  (Proof shortened by
-     Wolf Lammen, 15-Jun-2019.) $)
+     Wolf Lammen, 15-Jun-2019.)  (New usage is discouraged.) $)
   equvel $p |- ( A. z ( z = x <-> z = y ) -> x = y ) $=
     ( weq wb wal wex albi wi ax6e biimpr ax7 syli com12 eximii 19.35i spsd a1dd
     sps wn wa nfeqf 19.9d ex bija sylc ) CADZCBDZEZCFUGCFZUHCFZEABDZCGZULUGUHCH
@@ -21493,14 +21522,15 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
   $( A property related to substitution that unlike ~ equs5 does not require a
      distinctor antecedent.  See ~ equs5av and ~ equs5aALT for proofs using
-     ~ ax-12 but not ~ ax13 .  (Contributed by NM, 2-Feb-2007.) $)
+     ~ ax-12 but not ~ ax13 .  (Contributed by NM, 2-Feb-2007.)
+     (New usage is discouraged.) $)
   equs5a $p |- ( E. x ( x = y /\ A. y ph ) -> A. x ( x = y -> ph ) ) $=
     ( weq wal wa wi nfa1 ax12 imp exlimi ) BCDZACEZFLAGZBEZBNBHLMOABCIJK $.
 
   $( A property related to substitution that unlike ~ equs5 does not require a
      distinctor antecedent.  See ~ equs5eALT for an alternate proof using
      ~ ax-12 but not ~ ax13 .  (Contributed by NM, 2-Feb-2007.)  (Proof
-     shortened by Wolf Lammen, 15-Jan-2018.) $)
+     shortened by Wolf Lammen, 15-Jan-2018.)  (New usage is discouraged.) $)
   equs5e $p |- ( E. x ( x = y /\ ph ) -> A. x ( x = y -> E. y ph ) ) $=
     ( weq wa wex wi wal nfa1 ax12 hbe1 19.23bi impel exlimi ) BCDZAEOACFZGZBHZB
     QBIOPCHZRAPBCJASCACKLMN $.
@@ -21512,7 +21542,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
        non-freeness hypothesis.  Theorem ~ sb56 replaces the non-freeness
        hypothesis with a disjoint variable condition and ~ equs5 replaces it
        with a distinctor as antecedent.  (Contributed by NM, 25-Apr-2008.)
-       (Revised by Mario Carneiro, 4-Oct-2016.) $)
+       (Revised by Mario Carneiro, 4-Oct-2016.)  (New usage is discouraged.) $)
     equs45f $p |- ( E. x ( x = y /\ ph ) <-> A. x ( x = y -> ph ) ) $=
       ( weq wa wex wi wal nf5ri anim2i eximi equs5a syl equs4 impbii ) BCEZAFZB
       GZQAHBIZSQACIZFZBGTRUBBAUAQACDJKLABCMNABCOP $.
@@ -21521,7 +21551,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   $( Lemma used in proofs of substitution properties.  If there is a disjoint
      variable condition on ` x , y ` , then ~ sb56 can be used instead; if
      ` y ` is not free in ` ph ` , then ~ equs45f can be used.  (Contributed by
-     NM, 14-May-1993.)  (Revised by BJ, 1-Oct-2018.) $)
+     NM, 14-May-1993.)  (Revised by BJ, 1-Oct-2018.)
+     (New usage is discouraged.) $)
   equs5 $p |- ( -. A. x x = y ->
              ( E. x ( x = y /\ ph ) <-> A. x ( x = y -> ph ) ) ) $=
     ( weq wal wn wa wex wi nfna1 nfa1 axc15 impd exlimd equs4 impbid1 ) BCDZBEF
@@ -21530,12 +21561,12 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   ${
     $d w z x $.  $d w y $.
     $( Quantifier introduction when one pair of variables is distinct.
-       (Contributed by NM, 2-Jan-2002.) $)
+       (Contributed by NM, 2-Jan-2002.)  (New usage is discouraged.) $)
     dveel1 $p |- ( -. A. x x = y -> ( y e. z -> A. x y e. z ) ) $=
       ( vw wel elequ1 dvelimv ) DCEBCEABDDBCFG $.
 
     $( Quantifier introduction when one pair of variables is distinct.
-       (Contributed by NM, 2-Jan-2002.) $)
+       (Contributed by NM, 2-Jan-2002.)  (New usage is discouraged.) $)
     dveel2 $p |- ( -. A. x x = y -> ( z e. y -> A. x z e. y ) ) $=
       ( vw wel elequ2 dvelimv ) CDECBEABDDBCFG $.
   $}
@@ -21549,7 +21580,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
        purpose is to satisfy the distinct variable requirements of ~ dveel2 and
        ~ ax-5 .  By the end of the proof it has vanished, and the final theorem
        has no distinct variable requirements.  (Contributed by NM,
-       29-Jun-1995.)  (Proof modification is discouraged.) $)
+       29-Jun-1995.)  (Proof modification is discouraged.)
+       (New usage is discouraged.) $)
     axc14 $p |- ( -. A. z z = x -> ( -. A. z z = y ->
               ( x e. y -> A. z x e. y ) ) ) $=
       ( vw weq wal wn wel hbn1 dveel2 hbim1 elequ1 imbi2d dvelim nfa1 nfn 19.21
@@ -21561,19 +21593,19 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     sb6x.1 $e |- F/ x ph $.
     $( Equivalence involving substitution for a variable not free.
        (Contributed by NM, 2-Jun-1993.)  (Revised by Mario Carneiro,
-       4-Oct-2016.) $)
+       4-Oct-2016.)  (New usage is discouraged.) $)
     sb6x $p |- ( [ y / x ] ph <-> A. x ( x = y -> ph ) ) $=
       ( wsb weq wi wal sbf biidd equsal bitr4i ) ABCEABCFZAGBHABCDIAABCDMAJKL
       $.
   $}
 
   $( Substitution does not change an identical variable specifier.
-     (Contributed by NM, 15-May-1993.) $)
+     (Contributed by NM, 15-May-1993.)  (New usage is discouraged.) $)
   sbequ5 $p |- ( [ w / z ] A. x x = y <-> A. x x = y ) $=
     ( weq wal nfae sbf ) ABEAFCDABCGH $.
 
   $( Substitution does not change a distinctor.  (Contributed by NM,
-     5-Aug-1993.) $)
+     5-Aug-1993.)  (New usage is discouraged.) $)
   sbequ6 $p |- ( [ w / z ] -. A. x x = y <-> -. A. x x = y ) $=
     ( weq wal wn nfnae sbf ) ABEAFGCDABCHI $.
 
@@ -21581,14 +21613,14 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     sb5rf.1 $e |- F/ y ph $.
     $( Reversed substitution.  (Contributed by NM, 3-Feb-2005.)  (Revised by
        Mario Carneiro, 6-Oct-2016.)  (Proof shortened by Wolf Lammen,
-       20-Sep-2018.) $)
+       20-Sep-2018.)  (New usage is discouraged.) $)
     sb5rf $p |- ( ph <-> E. y ( y = x /\ [ y / x ] ph ) ) $=
       ( weq wsb wa wex sbequ12r equsex bicomi ) CBEABCFZGCHALACBDACBIJK $.
 
     $( Reversed substitution.  For a version requiring disjoint variables, but
        fewer axioms, see ~ sb6rfv .  (Contributed by NM, 1-Aug-1993.)  (Revised
        by Mario Carneiro, 6-Oct-2016.)  (Proof shortened by Wolf Lammen,
-       21-Sep-2018.) $)
+       21-Sep-2018.)  (New usage is discouraged.) $)
     sb6rf $p |- ( ph <-> A. y ( y = x -> [ y / x ] ph ) ) $=
       ( weq wsb wi wal sbequ12r equsal bicomi ) CBEABCFZGCHALACBDACBIJK $.
   $}
@@ -21608,7 +21640,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
      instances ` E. z z = x ` and ` E. w w = y ` into a common expression.
      Alan Sare contributed a variant of this theorem with distinct variable
      conditions before, see ~ ax6e2nd .  (Contributed by Wolf Lammen,
-     27-Sep-2018.) $)
+     27-Sep-2018.)  (New usage is discouraged.) $)
   2ax6elem $p |- ( -. A. w w = z -> E. z E. w ( z = x /\ w = y ) ) $=
     ( weq wal wn wex ax6e nfnae nfan nfeqf pm3.21 spimed eximd mpi nfae equvini
     wa ex equtrr anim1d aleximi syl5 pm2.61d2 ) DCEDFGZDAEZDFZCAEZDBEZSZDHZCHZU
@@ -21620,7 +21652,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     $( We can always find values matching ` x ` and ` y ` , as long as they are
        represented by distinct variables.  Version of ~ 2ax6elem with a
        distinct variable constraint.  (Contributed by Wolf Lammen,
-       28-Sep-2018.)  (Proof shortened by Wolf Lammen, 3-Oct-2023.) $)
+       28-Sep-2018.)  (Proof shortened by Wolf Lammen, 3-Oct-2023.)
+       (New usage is discouraged.) $)
     2ax6e $p |- E. z E. w ( z = x /\ w = y ) $=
       ( weq wal wa wex aeveq jca 19.8ad 2ax6elem pm2.61i ) DCEDFZCAEZDBEZGZDHZC
       HNRCNQDNOPDCCAIDCDBIJKKABCDLM $.
@@ -21639,7 +21672,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     2sb5rf.2 $e |- F/ w ph $.
     $( Reversed double substitution.  (Contributed by NM, 3-Feb-2005.)
        (Revised by Mario Carneiro, 6-Oct-2016.)  Remove distinct variable
-       constraints.  (Revised by Wolf Lammen, 28-Sep-2018.) $)
+       constraints.  (Revised by Wolf Lammen, 28-Sep-2018.)
+       (New usage is discouraged.) $)
     2sb5rf $p |- ( ph <->
                 E. z E. w ( ( z = x /\ w = y ) /\ [ z / x ] [ w / y ] ph ) ) $=
       ( weq wa wex 19.41 exbii 2ax6e biantrur 3bitr4ri sbequ12r sylan9bb 2exbii
@@ -21649,7 +21683,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     $( Reversed double substitution.  (Contributed by NM, 3-Feb-2005.)
        (Revised by Mario Carneiro, 6-Oct-2016.)  Remove variable constraints.
        (Revised by Wolf Lammen, 28-Sep-2018.)  (Proof shortened by Wolf Lammen,
-       13-Apr-2023.) $)
+       13-Apr-2023.)  (New usage is discouraged.) $)
     2sb6rf $p |- ( ph <->
                 A. z A. w ( ( z = x /\ w = y ) -> [ z / x ] [ w / y ] ph ) ) $=
       ( weq wa wi wal wsb wex 19.23 albii 2ax6e a1bi 3bitr4ri sbequ12r sylan9bb
@@ -21672,7 +21706,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   ${
     $d x y ph $.
     $( Elimination of double substitution.  (Contributed by NM, 5-Aug-1993.)
-       (Proof shortened by Wolf Lammen, 29-Sep-2018.) $)
+       (Proof shortened by Wolf Lammen, 29-Sep-2018.)
+       (New usage is discouraged.) $)
     sbel2x $p |- ( ph <-> E. x E. y ( ( x = z /\ y = w ) /\
                      [ y / w ] [ x / z ] ph ) ) $=
       ( weq wa wsb wex nfv 2sb5rf ancom anbi1i 2exbii excom 3bitri ) ACEFZBDFZG
@@ -21683,7 +21718,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     $d y x $.  $d y t $.  $d y ph $.
     $( Simplified definition of substitution when variables are distinct.
        Version of ~ sb6 with a distinctor.  (Contributed by NM, 27-May-1997.)
-       Revise ~ df-sb .  (Revised by Wolf Lammen, 21-Feb-2024.) $)
+       Revise ~ df-sb .  (Revised by Wolf Lammen, 21-Feb-2024.)
+       (New usage is discouraged.) $)
     sb4b $p |- ( -. A. x x = t -> ( [ t / x ] ph
                                               <-> A. x ( x = t -> ph ) ) ) $=
       ( vy weq wal wn wi wa nfna1 nfeqf2 nfan1 wb equequ2 imbi1d albid pm5.74da
@@ -21705,21 +21741,23 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
   $( Simplified definition of substitution when variables are distinct.  This
      is the biconditional strengthening of ~ sb3 .  (Contributed by BJ,
-     6-Oct-2018.)  Shorten ~ sb3 .  (Revised by Wolf Lammen, 21-Feb-2021.) $)
+     6-Oct-2018.)  Shorten ~ sb3 .  (Revised by Wolf Lammen, 21-Feb-2021.)
+     (New usage is discouraged.) $)
   sb3b $p |- ( -. A. x x = y -> ( [ y / x ] ph <-> E. x ( x = y /\ ph ) ) ) $=
     ( weq wal wn wsb wi wa wex sb4b equs5 bitr4d ) BCDZBEFABCGNAHBENAIBJABCKABC
     LM $.
 
   $( One direction of a simplified definition of substitution when variables
      are distinct.  (Contributed by NM, 5-Aug-1993.)  (Proof shortened by Wolf
-     Lammen, 21-Feb-2024.) $)
+     Lammen, 21-Feb-2024.)  (New usage is discouraged.) $)
   sb3 $p |- ( -. A. x x = y -> ( E. x ( x = y /\ ph ) -> [ y / x ] ph ) ) $=
     ( weq wal wn wsb wa wex sb3b biimprd ) BCDZBEFABCGLAHBIABCJK $.
 
   $( One direction of a simplified definition of substitution.  The converse
      requires either a disjoint variable condition ( ~ sb5 ) or a non-freeness
      hypothesis ( ~ sb5f ).  See also ~ sb1v .  (Contributed by NM,
-     13-May-1993.)  Revise ~ df-sb .  (Revised by Wolf Lammen, 21-Feb-2024.) $)
+     13-May-1993.)  Revise ~ df-sb .  (Revised by Wolf Lammen, 21-Feb-2024.)
+     (New usage is discouraged.) $)
   sb1 $p |- ( [ y / x ] ph -> E. x ( x = y /\ ph ) ) $=
     ( weq wal wsb wa wex wi spsbe pm3.2 aleximi syl5 wn sb3b biimpd pm2.61i ) B
     CDZBEZABCFZRAGZBHZITABHSUBABCJRAUABRAKLMSNTUBABCOPQ $.
@@ -21727,7 +21765,8 @@ requires either a disjoint variable condition ( ~ sb5 ) or a non-freeness
   $( One direction of a simplified definition of substitution.  The converse
      requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
      hypothesis ( ~ sb6f ).  (Contributed by NM, 13-May-1993.)  Revise
-     ~ df-sb .  (Revised by Wolf Lammen, 26-Jul-2023.) $)
+     ~ df-sb .  (Revised by Wolf Lammen, 26-Jul-2023.)
+     (New usage is discouraged.) $)
   sb2 $p |- ( A. x ( x = y -> ph ) -> [ y / x ] ph ) $=
     ( weq wal wi wsb pm2.27 al2imi stdpc4 syl6 wn sb4b biimprd pm2.61i ) BCDZBE
     ZPAFZBEZABCGZFQSABETPRABPAHIABCJKQLTSABCMNO $.
@@ -21764,7 +21803,7 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
 
   $( A version of one implication of ~ sb4b that does not require a distinctor
      antecedent.  (Contributed by NM, 2-Feb-2007.)  Revise ~ df-sb .  (Revised
-     by Wolf Lammen, 28-Jul-2023.) $)
+     by Wolf Lammen, 28-Jul-2023.)  (New usage is discouraged.) $)
   sb4a $p |- ( [ t / x ] A. t ph -> A. x ( x = t -> ph ) ) $=
     ( weq wal wsb wi sbequ2 sps axc11r ala1 syl6 syld wn sp imim2i alimi syl6bi
     sb4b pm2.61i ) BCDZBEZACEZBCFZUAAGZBEZGUBUDUCUFUAUDUCGBUCBCHIUBUCABEUFACBJA
@@ -21775,7 +21814,7 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
      Note that it does not require dummy variables in its definiens; this is
      done by having ` x ` free in the first conjunct and bound in the second.
      (Contributed by BJ, 9-Jul-2023.)  Revise ~ df-sb .  (Revised by Wolf
-     Lammen, 29-Jul-2023.) $)
+     Lammen, 29-Jul-2023.)  (New usage is discouraged.) $)
   dfsb1 $p |- ( [ y / x ] ph <->
                 ( ( x = y -> ph ) /\ E. x ( x = y /\ ph ) ) ) $=
     ( wsb weq wi wa wex sbequ2 com12 sb1 jca wal sbequ1 embantd sps adantrd sb3
@@ -21880,29 +21919,29 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
     IPBJABCKLM $.
 
   $( Bound-variable hypothesis builder for substitution.  (Contributed by NM,
-     14-May-1993.) $)
+     14-May-1993.)  (New usage is discouraged.) $)
   hbsb2 $p |- ( -. A. x x = y -> ( [ y / x ] ph -> A. x [ y / x ] ph ) ) $=
     ( weq wal wn wsb wi sb4b sb2 axc4i syl6bi ) BCDZBEFABCGZMAHZBENBEABCIONBABC
     JKL $.
 
   $( Bound-variable hypothesis builder for substitution.  (Contributed by Mario
-     Carneiro, 4-Oct-2016.) $)
+     Carneiro, 4-Oct-2016.)  (New usage is discouraged.) $)
   nfsb2 $p |- ( -. A. x x = y -> F/ x [ y / x ] ph ) $=
     ( weq wal wn wsb nfna1 hbsb2 nf5d ) BCDZBEFABCGBKBHABCIJ $.
 
   $( Special case of a bound-variable hypothesis builder for substitution.
-     (Contributed by NM, 2-Feb-2007.) $)
+     (Contributed by NM, 2-Feb-2007.)  (New usage is discouraged.) $)
   hbsb2a $p |- ( [ y / x ] A. y ph -> A. x [ y / x ] ph ) $=
     ( wal wsb weq wi sb4a sb2 axc4i syl ) ACDBCEBCFAGZBDABCEZBDABCHLMBABCIJK $.
 
   $( One direction of a simplified definition of substitution that unlike
      ~ sb4b does not require a distinctor antecedent.  (Contributed by NM,
-     2-Feb-2007.) $)
+     2-Feb-2007.)  (New usage is discouraged.) $)
   sb4e $p |- ( [ y / x ] ph -> A. x ( x = y -> E. y ph ) ) $=
     ( wsb weq wa wex wi wal sb1 equs5e syl ) ABCDBCEZAFBGMACGHBIABCJABCKL $.
 
   $( Special case of a bound-variable hypothesis builder for substitution.
-     (Contributed by NM, 2-Feb-2007.) $)
+     (Contributed by NM, 2-Feb-2007.)  (New usage is discouraged.) $)
   hbsb2e $p |- ( [ y / x ] ph -> A. x [ y / x ] E. y ph ) $=
     ( wsb weq wex wi wal sb4e sb2 axc4i syl ) ABCDBCEACFZGZBHMBCDZBHABCINOBMBCJ
     KL $.
@@ -21910,7 +21949,7 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
   ${
     hbsb3.1 $e |- ( ph -> A. y ph ) $.
     $( If ` y ` is not free in ` ph ` , ` x ` is not free in ` [ y / x ] ph ` .
-       (Contributed by NM, 14-May-1993.) $)
+       (Contributed by NM, 14-May-1993.)  (New usage is discouraged.) $)
     hbsb3 $p |- ( [ y / x ] ph -> A. x [ y / x ] ph ) $=
       ( wsb wal sbimi hbsb2a syl ) ABCEZACFZBCEJBFAKBCDGABCHI $.
   $}
@@ -21918,7 +21957,8 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
   ${
     nfs1.1 $e |- F/ y ph $.
     $( If ` y ` is not free in ` ph ` , ` x ` is not free in ` [ y / x ] ph ` .
-       (Contributed by Mario Carneiro, 11-Aug-2016.) $)
+       (Contributed by Mario Carneiro, 11-Aug-2016.)
+       (New usage is discouraged.) $)
     nfs1 $p |- F/ x [ y / x ] ph $=
       ( wsb nf5ri hbsb3 nf5i ) ABCEBABCACDFGH $.
   $}
@@ -21944,19 +21984,19 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
       BCDBDGABCHMONAADBMAIJKL $.
   $}
 
-  $( Substitution applied to an atomic wff.  (Contributed by NM,
-     10-May-1993.) $)
+  $( Substitution applied to an atomic wff.  (Contributed by NM, 10-May-1993.)
+     (New usage is discouraged.) $)
   equsb1 $p |- [ y / x ] x = y $=
     ( weq wi wsb sb2 id mpg ) ABCZIDIABEAIABFIGH $.
 
-  $( Substitution applied to an atomic wff.  (Contributed by NM,
-     10-May-1993.) $)
+  $( Substitution applied to an atomic wff.  (Contributed by NM, 10-May-1993.)
+     (New usage is discouraged.) $)
   equsb2 $p |- [ y / x ] y = x $=
     ( weq wi wsb sb2 equcomi mpg ) ABCBACZDIABEAIABFABGH $.
 
   $( An alternate definition of proper substitution that, like ~ dfsb1 , mixes
      free and bound variables to avoid distinct variable requirements.
-     (Contributed by NM, 17-Feb-2005.) $)
+     (Contributed by NM, 17-Feb-2005.)  (New usage is discouraged.) $)
   dfsb2 $p |- ( [ y / x ] ph <->
               ( ( x = y /\ ph ) \/ A. x ( x = y -> ph ) ) ) $=
     ( wsb weq wa wi wal wo sbequ2 sps orc syl6an sb4b olc syl6bi pm2.61i sbequ1
@@ -21965,7 +22005,7 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
 
   $( An alternate definition of proper substitution ~ df-sb that uses only
      primitive connectives (no defined terms) on the right-hand side.
-     (Contributed by NM, 6-Mar-2007.) $)
+     (Contributed by NM, 6-Mar-2007.)  (New usage is discouraged.) $)
   dfsb3 $p |- ( [ y / x ] ph <->
               ( ( x = y -> -. ph ) -> A. x ( x = y -> ph ) ) ) $=
     ( weq wa wi wal wo wn wsb df-or dfsb2 imnan imbi1i 3bitr4i ) BCDZAEZPAFBGZH
@@ -21983,7 +22023,7 @@ primitive connectives (no defined terms) on the right-hand side.
 
   $( Formula-building lemma for use with the Distinctor Reduction Theorem.
      Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).  (Contributed
-     by NM, 2-Jun-1993.) $)
+     by NM, 2-Jun-1993.)  (New usage is discouraged.) $)
   drsb1 $p |- ( A. x x = y -> ( [ z / x ] ph <-> [ z / y ] ph ) ) $=
     ( weq wal wi wa wex wsb wb equequ1 sps imbi1d anbi1d drex1 anbi12d 3bitr4g
     dfsb1 ) BCEZBFZBDEZAGZUBAHZBIZHCDEZAGZUFAHZCIZHABDJACDJUAUCUGUEUIUAUBUFATUB
@@ -21993,7 +22033,7 @@ primitive connectives (no defined terms) on the right-hand side.
     $d v y $.
     $( In the case of two successive substitutions for two always equal
        variables, the second substitution has no effect.  (Contributed by BJ
-       and WL, 9-Aug-2023.) $)
+       and WL, 9-Aug-2023.)  (New usage is discouraged.) $)
     sb2ae $p |-
                ( A. x x = y -> ( [ u / x ] [ v / y ] ph <-> [ v / y ] ph ) ) $=
       ( weq wal wsb drsb1 nfs1v sbf syl6bb ) BCFBGACDHZBEHMCEHMMBCEIMCEACDJKL
@@ -22006,7 +22046,7 @@ primitive connectives (no defined terms) on the right-hand side.
        implication "to the left" is ~ sb2 and does not require the non-freeness
        hypothesis.  Theorem ~ sb6 replaces the non-freeness hypothesis with a
        disjoint variable condition.  (Contributed by NM, 2-Jun-1993.)  (Revised
-       by Mario Carneiro, 4-Oct-2016.) $)
+       by Mario Carneiro, 4-Oct-2016.)  (New usage is discouraged.) $)
     sb6f $p |- ( [ y / x ] ph <-> A. x ( x = y -> ph ) ) $=
       ( wsb weq wi wal nf5ri sbimi sb4a syl sb2 impbii ) ABCEZBCFAGBHZOACHZBCEP
       AQBCACDIJABCKLABCMN $.
@@ -22015,7 +22055,8 @@ primitive connectives (no defined terms) on the right-hand side.
        implication "to the right" is ~ sb1 and does not require the
        non-freeness hypothesis.  Theorem ~ sb5 replaces the non-freeness
        hypothesis with a disjoint variable condition.  (Contributed by NM,
-       5-Aug-1993.)  (Revised by Mario Carneiro, 4-Oct-2016.) $)
+       5-Aug-1993.)  (Revised by Mario Carneiro, 4-Oct-2016.)
+       (New usage is discouraged.) $)
     sb5f $p |- ( [ y / x ] ph <-> E. x ( x = y /\ ph ) ) $=
       ( wsb weq wi wal wa wex sb6f equs45f bitr4i ) ABCEBCFZAGBHNAIBJABCDKABCDL
       M $.
@@ -22024,7 +22065,8 @@ primitive connectives (no defined terms) on the right-hand side.
   $( A variable not free in a proposition remains so after substitution in that
      proposition with a distinct variable (closed form of ~ nfsb4 ).
      (Contributed by NM, 7-Apr-2004.)  (Revised by Mario Carneiro, 4-Oct-2016.)
-     (Proof shortened by Wolf Lammen, 11-May-2018.) $)
+     (Proof shortened by Wolf Lammen, 11-May-2018.)
+     (New usage is discouraged.) $)
   nfsb4t $p |- ( A. x F/ z ph ->
                  ( -. A. z z = y -> F/ z [ y / x ] ph ) ) $=
     ( wnf wal weq wn wsb wi wa sbequ12 sps drnf2 biimpd spsd impcom nfnae nfan
@@ -22037,7 +22079,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     nfsb4.1 $e |- F/ z ph $.
     $( A variable not free in a proposition remains so after substitution in
        that proposition with a distinct variable.  (Contributed by NM,
-       14-May-1993.)  (Revised by Mario Carneiro, 4-Oct-2016.) $)
+       14-May-1993.)  (Revised by Mario Carneiro, 4-Oct-2016.)
+       (New usage is discouraged.) $)
     nfsb4 $p |- ( -. A. z z = y -> F/ z [ y / x ] ph ) $=
       ( wnf weq wal wn wsb wi nfsb4t mpg ) ADFDCGDHIABCJDFKBABCDLEM $.
   $}
@@ -22065,7 +22108,7 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
   $( Elimination of equality from antecedent after substitution.  (Contributed
      by NM, 5-Aug-1993.)  Reduce dependencies on axioms.  (Revised by Wolf
      Lammen, 28-Jul-2018.)  Revise ~ df-sb .  (Revised by Wolf Lammen,
-     28-Jul-2023.) $)
+     28-Jul-2023.)  (New usage is discouraged.) $)
   sbequ8 $p |- ( [ y / x ] ph <-> [ y / x ] ( x = y -> ph ) ) $=
     ( wsb weq wi equsb1 a1bi sbim bitr4i ) ABCDZBCEZBCDZKFLAFBCDMKBCGHLABCIJ $.
 
@@ -22075,8 +22118,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $( Conversion of implicit substitution to explicit substitution.  For
        versions requiring disjoint variables, but fewer axioms, see ~ sbiev and
        ~ sbievw .  (Contributed by NM, 30-Jun-1994.)  (Revised by Mario
-       Carneiro, 4-Oct-2016.)  (Proof shortened by Wolf Lammen,
-       13-Jul-2019.) $)
+       Carneiro, 4-Oct-2016.)  (Proof shortened by Wolf Lammen, 13-Jul-2019.)
+       (New usage is discouraged.) $)
     sbie $p |- ( [ y / x ] ph <-> ps ) $=
       ( wb wsb weq equsb1 sbimi ax-mp sbf sblbis mpbi ) ABGZCDHZACDHBGCDIZCDHQC
       DJRPCDFKLBBACDBCDEMNO $.
@@ -22090,7 +22133,7 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
        version of ~ sbie ) See ~ sbiedv , ~ sbiedw , ~ sbiedvw for variants
        using disjoint variables, but require fewer axioms.  (Contributed by NM,
        30-Jun-1994.)  (Revised by Mario Carneiro, 4-Oct-2016.)  (Proof
-       shortened by Wolf Lammen, 24-Jun-2018.) $)
+       shortened by Wolf Lammen, 24-Jun-2018.)  (New usage is discouraged.) $)
     sbied $p |- ( ph -> ( [ y / x ] ps <-> ch ) ) $=
       ( wsb wi sbrim nfim1 weq wb com12 pm5.74d sbie bitr3i pm5.74ri ) ABDEIZCA
       TJABJZDEIACJZABDEFKUAUBDEACDFGLDEMZABCAUCBCNHOPQRS $.
@@ -22101,7 +22144,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     sbiedv.1 $e |- ( ( ph /\ x = y ) -> ( ps <-> ch ) ) $.
     $( Conversion of implicit substitution to explicit substitution (deduction
        version of ~ sbie ).  See ~ sbied , ~ sbiedvw , ~ sbiedw for similar
-       variants (Contributed by NM, 7-Jan-2017.) $)
+       variants (Contributed by NM, 7-Jan-2017.)
+       (New usage is discouraged.) $)
     sbiedv $p |- ( ph -> ( [ y / x ] ps <-> ch ) ) $=
       ( nfv nfvd weq wb ex sbied ) ABCDEADGACDHADEIBCJFKL $.
   $}
@@ -22111,7 +22155,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     2sbiev.1 $e |- ( ( x = t /\ y = u ) -> ( ph <-> ps ) ) $.
     $( Conversion of double implicit substitution to explicit substitution.
        See ~ 2sbievw for a variant with extra disjoint variables, but based on
-       fewer axioms.  (Contributed by AV, 29-Jul-2023.) $)
+       fewer axioms.  (Contributed by AV, 29-Jul-2023.)
+       (New usage is discouraged.) $)
     2sbiev $p |- ( [ t / x ] [ u / y ] ph <-> ps ) $=
       ( wsb nfv weq sbiedv sbie ) ADEHBCFBCICFJABDEGKL $.
   $}
@@ -22121,7 +22166,7 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
      disjoint variables, but fewer axioms, see ~ sbcom3vv .  (Contributed by
      Giovanni Mascellani, 8-Apr-2018.)  Remove dependency on ~ ax-11 .
      (Revised by Wolf Lammen, 16-Sep-2018.)  (Proof shortened by Wolf Lammen,
-     16-Sep-2018.) $)
+     16-Sep-2018.)  (New usage is discouraged.) $)
   sbcom3 $p |- ( [ z / y ] [ y / x ] ph <-> [ z / y ] [ z / x ] ph ) $=
     ( weq wal wsb wb nfa1 drsb2 sbbid wn sb4b sbequ pm5.74i albii syl6bb bitr4d
     wi pm2.61i ) CDEZCFZABCGZCDGZABDGZCDGZHUBUCUECDUACIACDBJKUBLZUDUAUESZCFZUFU
@@ -22129,14 +22174,15 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
 
   $( A composition law for substitution.  See ~ sbcov for a version with a
      disjoint variable condition requiring fewer axioms.  (Contributed by NM,
-     14-May-1993.)  (Proof shortened by Wolf Lammen, 21-Sep-2018.) $)
+     14-May-1993.)  (Proof shortened by Wolf Lammen, 21-Sep-2018.)
+     (New usage is discouraged.) $)
   sbco $p |- ( [ y / x ] [ x / y ] ph <-> [ y / x ] ph ) $=
     ( wsb sbcom3 sbid sbbii bitri ) ACBDBCDACCDZBCDABCDACBCEIABCACFGH $.
 
   ${
     sbid2.1 $e |- F/ x ph $.
     $( An identity law for substitution.  (Contributed by NM, 14-May-1993.)
-       (Revised by Mario Carneiro, 6-Oct-2016.) $)
+       (Revised by Mario Carneiro, 6-Oct-2016.)  (New usage is discouraged.) $)
     sbid2 $p |- ( [ y / x ] [ x / y ] ph <-> ph ) $=
       ( wsb sbco sbf bitri ) ACBEBCEABCEAABCFABCDGH $.
   $}
@@ -22146,14 +22192,14 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $( An identity law for substitution.  Used in proof of Theorem 9.7 of
        [Megill] p. 449 (p. 16 of the preprint).  See ~ sbid2vw for a version
        with a disjoint variable condition requiring fewer axioms.  (Contributed
-       by NM, 5-Aug-1993.) $)
+       by NM, 5-Aug-1993.)  (New usage is discouraged.) $)
     sbid2v $p |- ( [ y / x ] [ x / y ] ph <-> ph ) $=
       ( nfv sbid2 ) ABCABDE $.
   $}
 
   $( An idempotent law for substitution.  (Contributed by NM, 30-Jun-1994.)
      (Proof shortened by Andrew Salmon, 25-May-2011.)  (Proof shortened by Wolf
-     Lammen, 13-Jul-2019.) $)
+     Lammen, 13-Jul-2019.)  (New usage is discouraged.) $)
   sbidm $p |- ( [ y / x ] [ y / x ] ph <-> [ y / x ] ph ) $=
     ( wsb sbcom3 sbid sbbii bitr3i ) ABCDZBCDABBDZBCDIABBCEJABCABFGH $.
 
@@ -22162,8 +22208,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $( A composition law for substitution.  For versions requiring fewer
        axioms, but more disjoint variable conditions, see ~ sbco2v and
        ~ sbco2vv .  (Contributed by NM, 30-Jun-1994.)  (Revised by Mario
-       Carneiro, 6-Oct-2016.)  (Proof shortened by Wolf Lammen,
-       17-Sep-2018.) $)
+       Carneiro, 6-Oct-2016.)  (Proof shortened by Wolf Lammen, 17-Sep-2018.)
+       (New usage is discouraged.) $)
     sbco2 $p |- ( [ y / z ] [ z / x ] ph <-> [ y / x ] ph ) $=
       ( weq wal wsb wb sbequ12 sbequ bitr3d sps wn nfnae nfsb4 wi sbied pm2.61i
       a1i ) DCFZDGZABDHZDCHZABCHZIZUAUFDUAUCUDUEUCDCJADCBKZLMUBNZUCUEDCDCDOABCD
@@ -22175,7 +22221,7 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     sbco2d.2 $e |- F/ z ph $.
     sbco2d.3 $e |- ( ph -> F/ z ps ) $.
     $( A composition law for substitution.  (Contributed by NM, 2-Jun-1993.)
-       (Revised by Mario Carneiro, 6-Oct-2016.) $)
+       (Revised by Mario Carneiro, 6-Oct-2016.)  (New usage is discouraged.) $)
     sbco2d $p |- ( ph -> ( [ y / z ] [ z / x ] ps <-> [ y / x ] ps ) ) $=
       ( wsb wi nfim1 sbco2 sbrim sbbii bitri 3bitr3i pm5.74ri ) ABCEIZEDIZBCDIZ
       ABJZCEIZEDIZUACDIASJZATJUACDEABEGHKLUCARJZEDIUDUBUEEDABCEFMNAREDGMOABCDFM
@@ -22183,7 +22229,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
   $}
 
   $( A composition law for substitution.  (Contributed by NM, 2-Jun-1993.)
-     (Proof shortened by Wolf Lammen, 18-Sep-2018.) $)
+     (Proof shortened by Wolf Lammen, 18-Sep-2018.)
+     (New usage is discouraged.) $)
   sbco3 $p |- ( [ z / y ] [ y / x ] ph <-> [ z / x ] [ x / y ] ph ) $=
     ( weq wal wsb wb drsb1 nfae sbequ12a sbbid bitr3d wn sbco sbbii nfnae nfsb2
     sps sbco2d syl5rbbr pm2.61i ) BCEZBFZABCGZCDGZACBGZBDGZHUDUEBDGUFUHUEBCDIUD
@@ -22191,14 +22238,16 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     UB $.
 
   $( A commutativity law for substitution.  (Contributed by NM, 27-May-1997.)
-     (Proof shortened by Wolf Lammen, 20-Sep-2018.) $)
+     (Proof shortened by Wolf Lammen, 20-Sep-2018.)
+     (New usage is discouraged.) $)
   sbcom $p |- ( [ y / z ] [ y / x ] ph <-> [ y / x ] [ y / z ] ph ) $=
     ( wsb sbco3 sbcom3 3bitr3i ) ABDEDCEADBEBCEABCEDCEADCEBCEABDCFABDCGADBCGH
     $.
 
   ${
     sbtrt.nf $e |- F/ y ph $.
-    $( Partially closed form of ~ sbtr .  (Contributed by BJ, 4-Jun-2019.) $)
+    $( Partially closed form of ~ sbtr .  (Contributed by BJ, 4-Jun-2019.)
+       (New usage is discouraged.) $)
     sbtrt $p |- ( A. y [ y / x ] ph -> ph ) $=
       ( wsb wal stdpc4 sbid2 sylib ) ABCEZCFJCBEAJCBGACBDHI $.
   $}
@@ -22208,7 +22257,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     sbtr.1 $e |- [ y / x ] ph $.
     $( A partial converse to ~ sbt .  If the substitution of a variable for a
        non-free one in a wff gives a theorem, then the original wff is a
-       theorem.  (Contributed by BJ, 15-Sep-2018.) $)
+       theorem.  (Contributed by BJ, 15-Sep-2018.)
+       (New usage is discouraged.) $)
     sbtr $p |- ph $=
       ( wsb sbtrt mpg ) ABCFACABCDGEH $.
   $}
@@ -22218,35 +22268,38 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $( Substitution of variable in universal quantifier.  For a version
        requiring disjoint variables, but fewer axioms, see ~ sb8v .
        (Contributed by NM, 16-May-1993.)  (Revised by Mario Carneiro,
-       6-Oct-2016.)  (Proof shortened by Jim Kingdon, 15-Jan-2018.) $)
+       6-Oct-2016.)  (Proof shortened by Jim Kingdon, 15-Jan-2018.)
+       (New usage is discouraged.) $)
     sb8 $p |- ( A. x ph <-> A. y [ y / x ] ph ) $=
       ( wsb nfs1 sbequ12 cbval ) AABCEBCDABCDFABCGH $.
 
     $( Substitution of variable in existential quantifier.  For a version
        requiring disjoint variables, but fewer axioms, see ~ sb8ev .
        (Contributed by NM, 12-Aug-1993.)  (Revised by Mario Carneiro,
-       6-Oct-2016.)  (Proof shortened by Jim Kingdon, 15-Jan-2018.) $)
+       6-Oct-2016.)  (Proof shortened by Jim Kingdon, 15-Jan-2018.)
+       (New usage is discouraged.) $)
     sb8e $p |- ( E. x ph <-> E. y [ y / x ] ph ) $=
       ( wsb nfs1 sbequ12 cbvex ) AABCEBCDABCDFABCGH $.
   $}
 
   $( Commutation of quantification and substitution variables.  (Contributed by
      NM, 5-Aug-1993.)  Allow a shortening of ~ sb9i .  (Revised by Wolf Lammen,
-     15-Jun-2019.) $)
+     15-Jun-2019.)  (New usage is discouraged.) $)
   sb9 $p |- ( A. x [ x / y ] ph <-> A. y [ y / x ] ph ) $=
     ( weq wal wsb wb sbequ12a equcoms sps dral1 wn nfnae wnf nfsb2 naecoms cbv2
     wi a1i pm2.61i ) BCDZBEZACBFZBEABCFZCEGUCUDBCUAUCUDGZBUECBACBHIZJKUBLZUCUDB
     CBCBMBCCMUCCNCBACBOPABCOUAUERUGUFSQT $.
 
   $( Commutation of quantification and substitution variables.  (Contributed by
-     NM, 5-Aug-1993.)  (Proof shortened by Wolf Lammen, 15-Jun-2019.) $)
+     NM, 5-Aug-1993.)  (Proof shortened by Wolf Lammen, 15-Jun-2019.)
+     (New usage is discouraged.) $)
   sb9i $p |- ( A. x [ x / y ] ph -> A. y [ y / x ] ph ) $=
     ( wsb wal sb9 biimpi ) ACBDBEABCDCEABCFG $.
 
   ${
     $d y ph $.
     $( Two ways of expressing " ` x ` is (effectively) not free in ` ph ` ".
-       (Contributed by NM, 29-May-2009.) $)
+       (Contributed by NM, 29-May-2009.)  (New usage is discouraged.) $)
     sbhb $p |- ( ( ph -> A. x ph ) <-> A. y ( ph -> [ y / x ] ph ) ) $=
       ( wal wi wsb nfv sb8 imbi2i 19.21v bitr4i ) AABDZEAABCFZCDZEAMECDLNAABCAC
       GHIAMCJK $.
@@ -22256,7 +22309,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $d y z $.
     nfsbd.1 $e |- F/ x ph $.
     nfsbd.2 $e |- ( ph -> F/ z ps ) $.
-    $( Deduction version of ~ nfsb .  (Contributed by NM, 15-Feb-2013.) $)
+    $( Deduction version of ~ nfsb .  (Contributed by NM, 15-Feb-2013.)
+       (New usage is discouraged.) $)
     nfsbd $p |- ( ph -> F/ z [ y / x ] ps ) $=
       ( weq wal wsb wnf wn wi alrimi nfsb4t syl axc16nf pm2.61d2 ) AEDHEIZBCDJZ
       EKZABEKZCISLUAMAUBCFGNBCDEOPTEDEQR $.
@@ -22268,8 +22322,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $( If ` z ` is not free in ` ph ` , it is not free in ` [ y / x ] ph ` when
        ` y ` and ` z ` are distinct.  For a version requiring more disjoint
        variables, but fewer axioms, see ~ nfsbv .  (Contributed by Mario
-       Carneiro, 11-Aug-2016.)  (Proof shortened by Wolf Lammen,
-       25-Feb-2024.) $)
+       Carneiro, 11-Aug-2016.)  (Proof shortened by Wolf Lammen, 25-Feb-2024.)
+       (New usage is discouraged.) $)
     nfsb $p |- F/ z [ y / x ] ph $=
       ( wsb wnf wtru nftru a1i nfsbd mptru ) ABCFDGHABCDBIADGHEJKL $.
 
@@ -22284,7 +22338,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $d y z $.
     hbsb.1 $e |- ( ph -> A. z ph ) $.
     $( If ` z ` is not free in ` ph ` , it is not free in ` [ y / x ] ph ` when
-       ` y ` and ` z ` are distinct.  (Contributed by NM, 12-Aug-1993.) $)
+       ` y ` and ` z ` are distinct.  (Contributed by NM, 12-Aug-1993.)
+       (New usage is discouraged.) $)
     hbsb $p |- ( [ y / x ] ph -> A. z [ y / x ] ph ) $=
       ( wsb nf5i nfsb nf5ri ) ABCFDABCDADEGHI $.
   $}
@@ -22298,7 +22353,7 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
        that doesn't have the concept of a variable not occurring in a wff.
        ( ~ dfsb1 is also suitable, but its mixing of free and bound variables
        is distasteful to some logicians.)  (Contributed by NM, 26-Jul-2006.)
-       (Revised by Mario Carneiro, 6-Oct-2016.) $)
+       (Revised by Mario Carneiro, 6-Oct-2016.)  (New usage is discouraged.) $)
     sb7f $p |- ( [ y / x ] ph <->
                E. z ( z = y /\ E. x ( x = z /\ ph ) ) ) $=
       ( wsb weq wa wex sb5f sbbii sbco2 sb5 3bitr3i ) ABDFZDCFBDGAHBIZDCFABCFDC
@@ -22314,7 +22369,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
        that doesn't have the concept of a variable not occurring in a wff.
        ( ~ dfsb1 is also suitable, but its mixing of free and bound variables
        is distasteful to some logicians.)  (Contributed by NM, 26-Jul-2006.)
-       (Proof shortened by Andrew Salmon, 25-May-2011.) $)
+       (Proof shortened by Andrew Salmon, 25-May-2011.)
+       (New usage is discouraged.) $)
     sb7h $p |- ( [ y / x ] ph <->
                E. z ( z = y /\ E. x ( x = z /\ ph ) ) ) $=
       ( nf5i sb7f ) ABCDADEFG $.
@@ -22346,7 +22402,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $( Hao Wang's identity axiom P6 in Irving Copi, _Symbolic Logic_ (5th ed.,
        1979), p. 328.  In traditional predicate calculus, this is a sole axiom
        for identity from which the usual ones can be derived.  (Contributed by
-       NM, 9-May-2005.)  (Revised by Mario Carneiro, 6-Oct-2016.) $)
+       NM, 9-May-2005.)  (Revised by Mario Carneiro, 6-Oct-2016.)
+       (New usage is discouraged.) $)
     sb10f $p |- ( [ y / z ] ph <-> E. x ( x = y /\ [ x / z ] ph ) ) $=
       ( weq wsb wa wex nfsb sbequ equsexv bicomi ) BCFADBGZHBIADCGZNOBCADCBEJAB
       CDKLM $.
@@ -22373,7 +22430,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $d z x $.
     $( Move quantifier in and out of substitution.  (Contributed by NM,
        2-Jan-2002.)  Remove a distinct variable constraint.  (Revised by Wolf
-       Lammen, 24-Dec-2022.)  (Proof shortened by Wolf Lammen, 23-Sep-2023.) $)
+       Lammen, 24-Dec-2022.)  (Proof shortened by Wolf Lammen, 23-Sep-2023.)
+       (New usage is discouraged.) $)
     sbal2 $p |- ( -. A. x x = y ->
              ( [ z / y ] A. x ph <-> A. x [ z / y ] ph ) ) $=
       ( weq wal wn wsb wb sbequ12 dral2 bitr3d adantl wa sb4b nfnae albid alcom
@@ -22411,7 +22469,7 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $d z w ph $.
     $( An equivalent expression for double existence.  For a version requiring
        more disjoint variables, but fewer axioms, see ~ 2sb8ev .  (Contributed
-       by Wolf Lammen, 2-Nov-2019.) $)
+       by Wolf Lammen, 2-Nov-2019.)  (New usage is discouraged.) $)
     2sb8e $p |- ( E. x E. y ph <->
                   E. z E. w [ z / x ] [ w / y ] ph ) $=
       ( wex wsb nfv sb8e exbii excom bitri nfsb 3bitri ) ACFZBFZACEGZBFZEFZQBDG
@@ -23056,7 +23114,7 @@ derived from that of uniqueness ( ~ df-mo ).  (Contributed by Wolf
     nfmod2.2 $e |- ( ( ph /\ -. A. x x = y ) -> F/ x ps ) $.
     $( Bound-variable hypothesis builder for the at-most-one quantifier.
        (Contributed by Mario Carneiro, 14-Nov-2016.)  Avoid ~ df-eu .  (Revised
-       by BJ, 14-Oct-2022.) $)
+       by BJ, 14-Oct-2022.)  (New usage is discouraged.) $)
     nfmod2 $p |- ( ph -> F/ x E* y ps ) $=
       ( vz wmo weq wi wal wex df-mo nfv wn wa wnf nfeqf1 adantl nfimd nfald2
       nfexd nfxfrd ) BDHBDGIZJZDKZGLACBDGMAUFCGAGNAUECDEACDICKOZPBUDCFUGUDCQACD
@@ -23092,7 +23150,7 @@ derived from that of uniqueness ( ~ df-mo ).  (Contributed by Wolf
     nfmod.2 $e |- ( ph -> F/ x ps ) $.
     $( Bound-variable hypothesis builder for the at-most-one quantifier.
        Deduction version of ~ nfmo .  (Contributed by Mario Carneiro,
-       14-Nov-2016.) $)
+       14-Nov-2016.)  (New usage is discouraged.) $)
     nfmod $p |- ( ph -> F/ x E* y ps ) $=
       ( wnf weq wal wn adantr nfmod2 ) ABCDEABCGCDHCIJFKL $.
   $}
@@ -23101,7 +23159,7 @@ derived from that of uniqueness ( ~ df-mo ).  (Contributed by Wolf
     nfmo.1 $e |- F/ x ph $.
     $( Bound-variable hypothesis builder for the at-most-one quantifier.  Note
        that ` x ` and ` y ` need not be disjoint.  (Contributed by NM,
-       9-Mar-1995.) $)
+       9-Mar-1995.)  (New usage is discouraged.) $)
     nfmo $p |- F/ x E* y ph $=
       ( wmo wnf wtru nftru a1i nfmod mptru ) ACEBFGABCCHABFGDIJK $.
   $}
@@ -23442,7 +23500,7 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     nfeud2.2 $e |- ( ( ph /\ -. A. x x = y ) -> F/ x ps ) $.
     $( Bound-variable hypothesis builder for uniqueness.  (Contributed by Mario
        Carneiro, 14-Nov-2016.)  (Proof shortened by Wolf Lammen, 4-Oct-2018.)
-       (Proof shortened by BJ, 14-Oct-2022.) $)
+       (Proof shortened by BJ, 14-Oct-2022.)  (New usage is discouraged.) $)
     nfeud2 $p |- ( ph -> F/ x E! y ps ) $=
       ( weu wex wmo wa df-eu nfexd2 nfmod2 nfand nfxfrd ) BDGBDHZBDIZJACBDKAPQC
       ABCDEFLABCDEFMNO $.
@@ -23465,7 +23523,7 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     nfeud.2 $e |- ( ph -> F/ x ps ) $.
     $( Bound-variable hypothesis builder for the unique existential quantifier.
        Deduction version of ~ nfeu .  (Contributed by NM, 15-Feb-2013.)
-       (Revised by Mario Carneiro, 7-Oct-2016.) $)
+       (Revised by Mario Carneiro, 7-Oct-2016.)  (New usage is discouraged.) $)
     nfeud $p |- ( ph -> F/ x E! y ps ) $=
       ( wnf weq wal wn adantr nfeud2 ) ABCDEABCGCDHCIJFKL $.
   $}
@@ -23484,7 +23542,8 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     nfeu.1 $e |- F/ x ph $.
     $( Bound-variable hypothesis builder for the unique existential quantifier.
        Note that ` x ` and ` y ` need not be disjoint.  (Contributed by NM,
-       8-Mar-1995.)  (Revised by Mario Carneiro, 7-Oct-2016.) $)
+       8-Mar-1995.)  (Revised by Mario Carneiro, 7-Oct-2016.)
+       (New usage is discouraged.) $)
     nfeu $p |- F/ x E! y ph $=
       ( weu wnf wtru nftru a1i nfeud mptru ) ACEBFGABCCHABFGDIJK $.
   $}
@@ -23554,12 +23613,13 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     $( Variable substitution in unique existential quantifier.  For a version
        requiring more disjoint variables, but fewer axioms, see ~ sb8euv .
        (Contributed by NM, 7-Aug-1994.)  (Revised by Mario Carneiro,
-       7-Oct-2016.)  (Proof shortened by Wolf Lammen, 24-Aug-2019.) $)
+       7-Oct-2016.)  (Proof shortened by Wolf Lammen, 24-Aug-2019.)
+       (New usage is discouraged.) $)
     sb8eu $p |- ( E! x ph <-> E! y [ y / x ] ph ) $=
       ( vw nfsb sb8eulem ) ABCEABECDFG $.
 
     $( Variable substitution for the at-most-one quantifier.  (Contributed by
-       Alexander van der Vekens, 17-Jun-2017.) $)
+       Alexander van der Vekens, 17-Jun-2017.)  (New usage is discouraged.) $)
     sb8mo $p |- ( E* x ph <-> E* y [ y / x ] ph ) $=
       ( wex weu wi wsb wmo sb8e sb8eu imbi12i moeu 3bitr4i ) ABEZABFZGABCHZCEZQ
       CFZGABIQCIORPSABCDJABCDKLABMQCMN $.
@@ -23585,7 +23645,8 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     cbvmo.3 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Rule used to change bound variables, using implicit substitution.
        (Contributed by NM, 9-Mar-1995.)  (Revised by Andrew Salmon,
-       8-Jun-2011.)  (Proof shortened by Wolf Lammen, 4-Jan-2023.) $)
+       8-Jun-2011.)  (Proof shortened by Wolf Lammen, 4-Jan-2023.)
+       (New usage is discouraged.) $)
     cbvmo $p |- ( E* x ph <-> E* y ps ) $=
       ( wmo wsb sb8mo sbie mobii bitri ) ACHACDIZDHBDHACDEJNBDABCDFGKLM $.
   $}
@@ -23608,7 +23669,7 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     cbveu.3 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Rule used to change bound variables, using implicit substitution.
        (Contributed by NM, 25-Nov-1994.)  (Revised by Mario Carneiro,
-       7-Oct-2016.) $)
+       7-Oct-2016.)  (New usage is discouraged.) $)
     cbveu $p |- ( E! x ph <-> E! y ps ) $=
       ( weu wsb sb8eu sbie eubii bitri ) ACHACDIZDHBDHACDEJNBDABCDFGKLM $.
 
@@ -23903,26 +23964,28 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     moexex.1 $e |- F/ y ph $.
     $( "At most one" double quantification.  (Contributed by NM, 3-Dec-2001.)
        (Proof shortened by Wolf Lammen, 28-Dec-2018.)  Factor out common proof
-       lines with ~ moexexvw .  (Revised by Wolf Lammen, 2-Oct-2023.) $)
+       lines with ~ moexexvw .  (Revised by Wolf Lammen, 2-Oct-2023.)
+       (New usage is discouraged.) $)
     moexex $p |- ( ( E* x ph /\ A. x E* y ps ) -> E* y E. x ( ph /\ ps ) ) $=
       ( nfmo wa wex nfe1 moexexlem ) ABCDEADCEFABGZCHCDKCIFJ $.
   $}
 
   ${
     $d y ph $.
-    $( "At most one" double quantification.  (Contributed by NM,
-       26-Jan-1997.) $)
+    $( "At most one" double quantification.  (Contributed by NM, 26-Jan-1997.)
+       (New usage is discouraged.) $)
     moexexv $p |- ( ( E* x ph /\ A. x E* y ps ) -> E* y E. x ( ph /\ ps ) ) $=
       ( nfv moexex ) ABCDADEF $.
   $}
 
   $( Double quantification with "at most one".  (Contributed by NM,
-     3-Dec-2001.) $)
+     3-Dec-2001.)  (New usage is discouraged.) $)
   2moex $p |- ( E* x E. y ph -> A. y E* x ph ) $=
     ( wex wmo nfe1 nfmo 19.8a moimi alrimi ) ACDZBEABECKCBACFGAKBACHIJ $.
 
   $( Double quantification with existential uniqueness.  (Contributed by NM,
-     3-Dec-2001.)  (Proof shortened by Andrew Salmon, 9-Jul-2011.) $)
+     3-Dec-2001.)  (Proof shortened by Andrew Salmon, 9-Jul-2011.)
+     (New usage is discouraged.) $)
   2euex $p |- ( E! x E. y ph -> E. y E! x ph ) $=
     ( wex weu wmo wa df-eu excom nfe1 nfmo 19.8a moimi moeu sylib syl5bi impcom
     wi eximd sylbi ) ACDZBEUABDZUABFZGABEZCDZUABHUCUBUEUBABDZCDUCUEABCIUCUFUDCU
@@ -23938,20 +24001,23 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     ( weu wex euex eximi syl ) ACDZBDIBEACEZBEIBFIJBACFGH $.
 
   $( A condition allowing to swap an existential quantifier and at at-most-one
-     quantifier.  (Contributed by NM, 10-Apr-2004.) $)
+     quantifier.  (Contributed by NM, 10-Apr-2004.)
+     (New usage is discouraged.) $)
   2moswap $p |- ( A. x E* y ph -> ( E* x E. y ph -> E* y E. x ph ) ) $=
     ( wmo wal wex wa nfe1 moexex expcom 19.8a pm4.71ri exbii mobii syl6ibr ) AC
     DBEZACFZBDZQAGZBFZCDZABFZCDRPUAQABCACHIJUBTCASBAQACKLMNO $.
 
   $( A condition allowing to swap an existential quantifier and a unique
-     existential quantifier.  (Contributed by NM, 10-Apr-2004.) $)
+     existential quantifier.  (Contributed by NM, 10-Apr-2004.)
+     (New usage is discouraged.) $)
   2euswap $p |- ( A. x E* y ph -> ( E! x E. y ph -> E! y E. x ph ) ) $=
     ( wmo wal wex wa weu wi excomim a1i 2moswap anim12d df-eu 3imtr4g ) ACDBEZA
     CFZBFZQBDZGABFZCFZTCDZGQBHTCHPRUASUBRUAIPABCJKABCLMQBNTCNO $.
 
   $( Double existential uniqueness implies double unique existential
      quantification.  The converse does not hold.  (Contributed by NM,
-     3-Dec-2001.)  (Proof shortened by Mario Carneiro, 22-Dec-2016.) $)
+     3-Dec-2001.)  (Proof shortened by Mario Carneiro, 22-Dec-2016.)
+     (New usage is discouraged.) $)
   2exeu $p |- ( ( E! x E. y ph /\ E! y E. x ph ) -> E! x E! y ph ) $=
     ( wex weu wa wmo eumo euex moimi syl 2euex anim12ci df-eu sylibr ) ACDZBEZA
     BDCEZFACEZBDZSBGZFSBEQUARTQPBGUAPBHSPBACIJKACBLMSBNO $.
@@ -24010,7 +24076,8 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
 
   $( Double existential uniqueness.  This theorem shows a condition under which
      a "naive" definition matches the correct one.  (Contributed by NM,
-     3-Dec-2001.)  (Proof shortened by Wolf Lammen, 23-Apr-2023.) $)
+     3-Dec-2001.)  (Proof shortened by Wolf Lammen, 23-Apr-2023.)
+     (New usage is discouraged.) $)
   2eu1 $p |- ( A. x E* y ph ->
         ( E! x E! y ph <-> ( E! x E. y ph /\ E! y E. x ph ) ) ) $=
     ( wmo wal weu wex wa wi 2eu2ex moeu albii euim sylan2b pm2.43b 2euswap syld
@@ -24041,14 +24108,15 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     $( $j usage '2eu1v' avoids 'ax-13'; $)
   $}
 
-  $( Double existential uniqueness.  (Contributed by NM, 3-Dec-2001.) $)
+  $( Double existential uniqueness.  (Contributed by NM, 3-Dec-2001.)
+     (New usage is discouraged.) $)
   2eu2 $p |- ( E! y E. x ph -> ( E! x E! y ph <-> E! x E. y ph ) ) $=
     ( wex weu wmo wal wi eumo 2moex 2eu1 simpl syl6bi 3syl 2exeu expcom impbid
     wa ) ABDZCEZACEBEZACDBEZTSCFACFBGZUAUBHSCIACBJUCUAUBTRUBABCKUBTLMNUBTUAABCO
     PQ $.
 
   $( Double existential uniqueness.  (Contributed by NM, 3-Dec-2001.)  (Proof
-     shortened by Wolf Lammen, 23-Apr-2023.) $)
+     shortened by Wolf Lammen, 23-Apr-2023.)  (New usage is discouraged.) $)
   2eu3 $p |- ( A. x A. y ( E* x ph \/ E* y ph ) ->
  ( ( E! x E! y ph /\ E! y E! x ph ) <-> ( E! x E. y ph /\ E! y E. x ph ) ) ) $=
     ( wmo wo wal weu wa wb nfmo1 19.31 albii nfal 19.32 bitri 2eu1 biimpd ancom
@@ -24130,7 +24198,7 @@ correct definition apparently has never been published ( ` E* ` means
   $}
 
   $( Two equivalent expressions for double existential uniqueness.
-     (Contributed by NM, 19-Feb-2005.) $)
+     (Contributed by NM, 19-Feb-2005.)  (New usage is discouraged.) $)
   2eu7 $p |- ( ( E! x E. y ph /\ E! y E. x ph ) <->
              E! x E! y ( E. x ph /\ E. y ph ) ) $=
     ( wex weu wa nfe1 nfeu euan ancom eubii 3bitri 3bitr4ri ) ABDZCEZACDZFZBEOP
@@ -24139,7 +24207,7 @@ correct definition apparently has never been published ( ` E* ` means
   $( Two equivalent expressions for double existential uniqueness.  Curiously,
      we can put ` E! ` on either of the internal conjuncts but not both.  We
      can also commute ` E! x E! y ` using ~ 2eu7 .  (Contributed by NM,
-     20-Feb-2005.) $)
+     20-Feb-2005.)  (New usage is discouraged.) $)
   2eu8 $p |- ( E! x E! y ( E. x ph /\ E. y ph ) <->
                 E! x E! y ( E! x ph /\ E. y ph ) ) $=
     ( wex wa 2eu2 pm5.32i nfeu1 nfeu euan ancom eubii nfe1 3bitri 3bitr4ri 2eu7
@@ -24877,7 +24945,7 @@ number of additional axioms (mainly to replace definitions like ~ df-or and
      additional quantifier).  But in intuitionistic logic, changing the
      negations and implications to disjunctions makes it stronger.
      (Contributed by Jim Kingdon, 31-Dec-2017.)  Avoid ~ ax-11 .  (Revised by
-     Wolf Lammen, 24-Apr-2023.) $)
+     Wolf Lammen, 24-Apr-2023.)  (New usage is discouraged.) $)
   axi12 $p |- ( A. z z = x \/ ( A. z z = y \/
                 A. z ( x = y -> A. z x = y ) ) ) $=
     ( weq wal wo wi nfa1 nfor 19.32 wn axc9 orrd orri orass mpbir mpgbi mpbi )
@@ -24898,7 +24966,7 @@ number of additional axioms (mainly to replace definitions like ~ df-or and
      ~ axc9 .  But in intuitionistic logic, it is not easy to add the extra
      ` A. x ` to ~ axi12 and so we treat the two as separate axioms.
      (Contributed by Jim Kingdon, 22-Mar-2018.)  (Proof shortened by Wolf
-     Lammen, 24-Apr-2023.) $)
+     Lammen, 24-Apr-2023.)  (New usage is discouraged.) $)
   axbnd $p |- ( A. z z = x \/ ( A. z z = y \/
                  A. x A. z ( x = y -> A. z x = y ) ) ) $=
     ( weq wal wo wi nfae nfor 19.32 orass bitri axi12 mpbir mpgbi ) CADCEZCBDCE
@@ -25289,7 +25357,8 @@ yield an eliminable and weakly (that is, object-level) conservative
     hbabg.1 $e |- ( ph -> A. x ph ) $.
     $( Bound-variable hypothesis builder for a class abstraction.  See ~ hbab
        for a version with more disjoint variable conditions, but not requiring
-       ~ ax-13 .  (Contributed by NM, 1-Mar-1995.) $)
+       ~ ax-13 .  (Contributed by NM, 1-Mar-1995.)
+       (New usage is discouraged.) $)
     hbabg $p |- ( z e. { y | ph } -> A. x z e. { y | ph } ) $=
       ( cv cab wcel wsb df-clab hbsb hbxfrbi ) DFACGHACDIBADCJACDBEKL $.
   $}
@@ -25311,7 +25380,8 @@ yield an eliminable and weakly (that is, object-level) conservative
     nfsabg.1 $e |- F/ x ph $.
     $( Bound-variable hypothesis builder for a class abstraction.  See ~ nfsab
        for a version with more disjoint variable conditions, but not requiring
-       ~ ax-13 .  (Contributed by Mario Carneiro, 11-Aug-2016.) $)
+       ~ ax-13 .  (Contributed by Mario Carneiro, 11-Aug-2016.)
+       (New usage is discouraged.) $)
     nfsabg $p |- F/ x z e. { y | ph } $=
       ( cv cab wcel nf5ri hbabg nf5i ) DFACGHBABCDABEIJK $.
   $}
@@ -26307,7 +26377,7 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     cbvabw $p |- { x | ph } = { y | ps } $=
       ( vz cab wsb cv wcel sbco2v sbiev sbbii bitr3i df-clab 3bitr4i eqriv ) HA
       CIZBDIZACHJZBDHJZHKZTLUDUALUBACDJZDHJUCACHDEMUEBDHABCDFGNOPAHCQBHDQRS $.
-    $( $j usage 'cbvabw' avoids 'ax-13'; $)
+    $( $j usage 'cbvabw' avoids 'ax-8' 'ax-13' 'df-clel'; $)
   $}
 
   ${
@@ -26317,7 +26387,7 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     cbvab.3 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Rule used to change bound variables, using implicit substitution.
        (Contributed by Andrew Salmon, 11-Jul-2011.)  (Proof shortened by Wolf
-       Lammen, 16-Nov-2019.) $)
+       Lammen, 16-Nov-2019.)  (New usage is discouraged.) $)
     cbvab $p |- { x | ph } = { y | ps } $=
       ( vz cab wsb cv wcel sbco2 sbie sbbii bitr3i df-clab 3bitr4i eqriv ) HACI
       ZBDIZACHJZBDHJZHKZTLUDUALUBACDJZDHJUCACHDEMUEBDHABCDFGNOPAHCQBHDQRS $.
@@ -26842,7 +26912,7 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     $( Change the free variable of a hypothesis builder.  See ~ hblem for a
        version with more disjoint variable conditions, but not requiring
        ~ ax-13 .  (Contributed by NM, 21-Jun-1993.)  (Revised by Andrew Salmon,
-       11-Jul-2011.) $)
+       11-Jul-2011.)  (New usage is discouraged.) $)
     hblemg $p |- ( z e. A -> A. x z e. A ) $=
       ( cv wcel wsb wal hbsb clelsb3 albii 3imtr3i ) BFDGZBCHZOAICFDGZPAINBCAEJ
       BCDKZOPAQLM $.
@@ -27252,7 +27322,8 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
        ~ clelsb3fw not requiring ~ ax-13 , but extra disjoint variables.
        (Contributed by Rodolfo Medina, 28-Apr-2010.)  (Proof shortened by
        Andrew Salmon, 14-Jun-2011.)  (Revised by Thierry Arnoux, 13-Mar-2017.)
-       (Proof shortened by Wolf Lammen, 7-May-2023.) $)
+       (Proof shortened by Wolf Lammen, 7-May-2023.)
+       (New usage is discouraged.) $)
     clelsb3f $p |- ( [ y / x ] x e. A <-> y e. A ) $=
       ( vw cv wcel wsb nfcri sbco2 clelsb3 sbbii 3bitr3i ) EFCGZEAHZABHNEBHAFCG
       ZABHBFCGNEBAAECDIJOPABEACKLEBCKM $.
@@ -27283,7 +27354,8 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     nfabg.1 $e |- F/ x ph $.
     $( Bound-variable hypothesis builder for a class abstraction.  See ~ nfab
        for a version with more disjoint variable conditions, but not requiring
-       ~ ax-13 .  (Contributed by Mario Carneiro, 11-Aug-2016.) $)
+       ~ ax-13 .  (Contributed by Mario Carneiro, 11-Aug-2016.)
+       (New usage is discouraged.) $)
     nfabg $p |- F/_ x { y | ph } $=
       ( vz cab nfsabg nfci ) BEACFABCEDGH $.
   $}
@@ -27301,7 +27373,8 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
 
   $( Bound-variable hypothesis builder for a class abstraction.  See ~ nfaba1
      for a version with disjoint variable conditions, but not requiring
-     ~ ax-13 .  (Contributed by Mario Carneiro, 14-Oct-2016.) $)
+     ~ ax-13 .  (Contributed by Mario Carneiro, 14-Oct-2016.)
+     (New usage is discouraged.) $)
   nfaba1g $p |- F/_ x { y | A. x ph } $=
     ( wal nfa1 nfabg ) ABDBCABEF $.
 
@@ -27380,7 +27453,7 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     drnfc1.1 $e |- ( A. x x = y -> A = B ) $.
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
        (Contributed by Mario Carneiro, 8-Oct-2016.)  Avoid ~ ax-11 .  (Revised
-       by Wolf Lammen, 10-May-2023.) $)
+       by Wolf Lammen, 10-May-2023.)  (New usage is discouraged.) $)
     drnfc1 $p |- ( A. x x = y -> ( F/_ x A <-> F/_ y B ) ) $=
       ( vw weq wal cv wcel wnf wnfc eleq2d drnf1 albidv df-nfc 3bitr4g ) ABGAHZ
       FIZCJZAKZFHSDJZBKZFHACLBDLRUAUCFTUBABRCDSEMNOAFCPBFDPQ $.
@@ -27397,7 +27470,8 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
        Proof revision is marked as discouraged because the minimizer replaces
        ~ albidv with ~ dral2 , leading to a one byte longer proof.  However
        feel free to manually edit it according to conventions.  (Contributed by
-       Mario Carneiro, 8-Oct-2016.)  (Proof modification is discouraged.) $)
+       Mario Carneiro, 8-Oct-2016.)  (Proof modification is discouraged.)
+       (New usage is discouraged.) $)
     drnfc2 $p |- ( A. x x = y -> ( F/_ z A <-> F/_ z B ) ) $=
       ( vw weq wal cv wcel wnf wnfc eleq2d drnf2 albidv df-nfc 3bitr4g ) ABHAIZ
       GJZDKZCLZGITEKZCLZGICDMCEMSUBUDGUAUCABCSDETFNOPCGDQCGEQR $.
@@ -27416,7 +27490,7 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
       ABCNZDOZVDCNZAVEDEFPVFVFVDQZCNVGVHDGRZVFBQZQZDOZCVLVHVJVHDGVFVDDVEDUAZVFV
       DDVMVFVDVIBQZDOZVDDOVDVOUBVFBDGUCZUOVNVDDVDVOVPUDUEUFUGSVIBVDVFBDGUHUIUJU
       KVKCDVIVJCVICIVFBCVECDBCULTZVEDUMSUNTUPVFVHVDCVQVFVDUQURUSUTVAVB $.
-    $( $j usage 'nfabdw' avoids 'ax-13'; $)
+    $( $j usage 'nfabdw' avoids 'ax-9' 'ax-13' 'ax-ext'; $)
   $}
 
   ${
@@ -27425,7 +27499,7 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     nfabd.2 $e |- ( ph -> F/ x ps ) $.
     $( Bound-variable hypothesis builder for a class abstraction.  (Contributed
        by Mario Carneiro, 8-Oct-2016.)  Avoid ~ ax-9 and ~ ax-ext .  (Revised
-       by Wolf Lammen, 23-May-2023.) $)
+       by Wolf Lammen, 23-May-2023.)  (New usage is discouraged.) $)
     nfabd $p |- ( ph -> F/_ x { y | ps } ) $=
       ( vz cab nfv cv wcel wsb df-clab nfsbd nfxfrd nfcd ) ACGBDHZAGIGJQKBDGLAC
       BGDMABDGCEFNOP $.
@@ -27437,7 +27511,7 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     nfabd2.2 $e |- ( ( ph /\ -. A. x x = y ) -> F/ x ps ) $.
     $( Bound-variable hypothesis builder for a class abstraction.  (Contributed
        by Mario Carneiro, 8-Oct-2016.)  (Proof shortened by Wolf Lammen,
-       10-May-2023.) $)
+       10-May-2023.)  (New usage is discouraged.) $)
     nfabd2 $p |- ( ph -> F/_ x { y | ps } ) $=
       ( weq wal cab wnfc wn wa nfnae nfan nfabd ex nfab1 eqidd drnfc1 mpbiri
       pm2.61d2 ) ACDGCHZCBDIZJZAUBKZUDAUELBCDAUEDECDDMNFOPUBUDDUCJBDQCDUCUCUBUC
@@ -27472,7 +27546,7 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     dvelimdc.4 $e |- ( ph -> F/_ z B ) $.
     dvelimdc.5 $e |- ( ph -> ( z = y -> A = B ) ) $.
     $( Deduction form of ~ dvelimc .  (Contributed by Mario Carneiro,
-       8-Oct-2016.) $)
+       8-Oct-2016.)  (New usage is discouraged.) $)
     dvelimdc $p |- ( ph -> ( -. A. x x = y -> F/_ x B ) ) $=
       ( vw weq wal wn wnfc wa nfv wcel nfcrd cv wnf wceq wb eleq2 syl6 dvelimdf
       imp nfcd ex ) ABCMBNOZBFPAUKQZBLFULLRAUKLUAZFSZBUBAUMESZUNBCDGHABLEITADLF
@@ -27484,7 +27558,7 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     dvelimc.2 $e |- F/_ z B $.
     dvelimc.3 $e |- ( z = y -> A = B ) $.
     $( Version of ~ dvelim for classes.  (Contributed by Mario Carneiro,
-       8-Oct-2016.) $)
+       8-Oct-2016.)  (New usage is discouraged.) $)
     dvelimc $p |- ( -. A. x x = y -> F/_ x B ) $=
       ( weq wal wn wnfc wi wtru nftru a1i wceq dvelimdc mptru ) ABIAJKAELMNABCD
       EAOCOADLNFPCELNGPCBIDEQMNHPRS $.
@@ -27494,14 +27568,15 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     $d x w z $.  $d y w z $.
     $( If ` x ` and ` y ` are distinct, then ` x ` is not free in ` y ` .
        (Contributed by Mario Carneiro, 8-Oct-2016.)  Avoid ~ ax-ext .  (Revised
-       by Wolf Lammen, 10-May-2023.) $)
+       by Wolf Lammen, 10-May-2023.)  (New usage is discouraged.) $)
     nfcvf $p |- ( -. A. x x = y -> F/_ x y ) $=
       ( vw vz weq wal wn cv nfv wel elequ2 dvelimnf nfcd ) ABEAFGZACBHNCICDJZCB
       JABDOAIDBCKLM $.
     $( $j usage 'nfcvf' avoids 'ax-ext'; $)
 
     $( If ` x ` and ` y ` are distinct, then ` y ` is not free in ` x ` .
-       (Contributed by Mario Carneiro, 5-Dec-2016.) $)
+       (Contributed by Mario Carneiro, 5-Dec-2016.)
+       (New usage is discouraged.) $)
     nfcvf2 $p |- ( -. A. x x = y -> F/_ y x ) $=
       ( cv wnfc nfcvf naecoms ) BACDBABAEF $.
   $}
@@ -29286,7 +29361,7 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     nfrald.2 $e |- ( ph -> F/_ x A ) $.
     nfrald.3 $e |- ( ph -> F/ x ps ) $.
     $( Deduction version of ~ nfral .  (Contributed by NM, 15-Feb-2013.)
-       (Revised by Mario Carneiro, 7-Oct-2016.) $)
+       (Revised by Mario Carneiro, 7-Oct-2016.)  (New usage is discouraged.) $)
     nfrald $p |- ( ph -> F/ x A. y e. A ps ) $=
       ( wral cv wcel wi wal df-ral weq wn wa wnfc nfcvf adantr adantl nfeld wnf
       nfimd nfald2 nfxfrd ) BDEIDJZEKZBLZDMACBDENAUICDFACDOCMPZQZUHBCUKCUGEUJCU
@@ -29310,7 +29385,7 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     nfral.2 $e |- F/ x ph $.
     $( Bound-variable hypothesis builder for restricted quantification.
        (Contributed by NM, 1-Sep-1999.)  (Revised by Mario Carneiro,
-       7-Oct-2016.) $)
+       7-Oct-2016.)  (New usage is discouraged.) $)
     nfral $p |- F/ x A. y e. A ph $=
       ( wral wnf wtru nftru wnfc a1i nfrald mptru ) ACDGBHIABCDCJBDKIELABHIFLMN
       $.
@@ -29329,8 +29404,8 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     $d A y $.
     $( Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the
        antecedent is restricted.  Derived automatically from ~ hbra2VD .
-       Contributed by Alan Sare 31-Dec-2011.  (Contributed by NM,
-       31-Dec-2011.) $)
+       Contributed by Alan Sare 31-Dec-2011.  (Contributed by NM, 31-Dec-2011.)
+       (New usage is discouraged.) $)
     nfra2 $p |- F/ y A. x e. A A. y e. B ph $=
       ( wral nfcv nfra1 nfral ) ACEFCBDCDGACEHI $.
   $}
@@ -29342,7 +29417,8 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
        ` y ` are not required to be disjoint.  This proof illustrates the use
        of ~ dvelim .  (Contributed by NM, 23-Nov-1994.)  (Proof shortened by
        Andrew Salmon, 25-May-2011.)  (Proof shortened by Wolf Lammen,
-       1-Jan-2020.)  (Proof modification is discouraged.) $)
+       1-Jan-2020.)  (Proof modification is discouraged.)
+       (New usage is discouraged.) $)
     rgen2a $p |- A. x e. A A. y e. A ph $=
       ( vz wral cv wcel wi wal weq wn eleq1 dvelimv alimi syl6com biimpd syli
       ex pm2.61d2 df-ral sylibr rgen ) ACDGZBDBHZDIZCHZDIZAJZCKZUEUGCBLZCKZUKUM
@@ -30041,7 +30117,7 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     nfrexdg.3 $e |- ( ph -> F/ x ps ) $.
     $( Deduction version of ~ nfrexg .  See ~ nfrexd for a version with
        disjoint variable conditions, but not requiring ~ ax-13 .  (Contributed
-       by Mario Carneiro, 14-Oct-2016.) $)
+       by Mario Carneiro, 14-Oct-2016.)  (New usage is discouraged.) $)
     nfrexdg $p |- ( ph -> F/ x E. y e. A ps ) $=
       ( wrex wn wral dfrex2 nfnd nfrald nfxfrd ) BDEIBJZDEKZJACBDELAQCAPCDEFGAB
       CHMNMO $.
@@ -30069,8 +30145,8 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     $( Bound-variable hypothesis builder for restricted quantification.  See
        ~ nfrex for a version with disjoint variable conditions, but not
        requiring ~ ax-13 .  (Contributed by NM, 1-Sep-1999.)  (Revised by Mario
-       Carneiro, 7-Oct-2016.)  (Proof shortened by Wolf Lammen,
-       30-Dec-2019.) $)
+       Carneiro, 7-Oct-2016.)  (Proof shortened by Wolf Lammen, 30-Dec-2019.)
+       (New usage is discouraged.) $)
     nfrexg $p |- F/ x E. y e. A ph $=
       ( wrex wnf wtru nftru wnfc a1i nfrexdg mptru ) ACDGBHIABCDCJBDKIELABHIFLM
       N $.
@@ -30593,7 +30669,8 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     $( Commutation of restricted universal quantifiers.  Note that ` x ` and
        ` y ` need not be disjoint (this makes the proof longer).  If ` x ` and
        ` y ` are disjoint, then one may use ~ ralcom .  (Contributed by NM,
-       24-Nov-1994.)  (Proof shortened by Mario Carneiro, 17-Oct-2016.) $)
+       24-Nov-1994.)  (Proof shortened by Mario Carneiro, 17-Oct-2016.)
+       (New usage is discouraged.) $)
     ralcom2 $p |- ( A. x e. A A. y e. A ph -> A. y e. A A. x e. A ph ) $=
       ( weq wal wral wi cv wcel wb eleq1w dral1 df-ral 3bitr4g wa nfnae ralrimi
       nfan ex sps imbi1d bicomd imbi12d biimpd wn nfra2 nfra1 wnfc nfcvf adantr
@@ -30686,13 +30763,14 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     nfreud.2 $e |- ( ph -> F/_ x A ) $.
     nfreud.3 $e |- ( ph -> F/ x ps ) $.
     $( Deduction version of ~ nfreu .  (Contributed by NM, 15-Feb-2013.)
-       (Revised by Mario Carneiro, 8-Oct-2016.) $)
+       (Revised by Mario Carneiro, 8-Oct-2016.)  (New usage is discouraged.) $)
     nfreud $p |- ( ph -> F/ x E! y e. A ps ) $=
       ( wreu cv wcel wa weu df-reu weq wal wn wnfc nfcvf adantr nfeld wnf nfand
       adantl nfeud2 nfxfrd ) BDEIDJZEKZBLZDMACBDENAUICDFACDOCPQZLZUHBCUKCUGEUJC
       UGRACDSUDACERUJGTUAABCUBUJHTUCUEUF $.
 
-    $( Deduction version of ~ nfrmo .  (Contributed by NM, 17-Jun-2017.) $)
+    $( Deduction version of ~ nfrmo .  (Contributed by NM, 17-Jun-2017.)
+       (New usage is discouraged.) $)
     nfrmod $p |- ( ph -> F/ x E* y e. A ps ) $=
       ( wrmo cv wcel wa wmo df-rmo weq wal wn wnfc nfcvf adantr nfeld wnf nfand
       adantl nfmod2 nfxfrd ) BDEIDJZEKZBLZDMACBDENAUICDFACDOCPQZLZUHBCUKCUGEUJC
@@ -30725,13 +30803,13 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     nfreu.2 $e |- F/ x ph $.
     $( Bound-variable hypothesis builder for restricted unique existence.
        (Contributed by NM, 30-Oct-2010.)  (Revised by Mario Carneiro,
-       8-Oct-2016.) $)
+       8-Oct-2016.)  (New usage is discouraged.) $)
     nfreu $p |- F/ x E! y e. A ph $=
       ( wreu wnf wtru nftru wnfc a1i nfreud mptru ) ACDGBHIABCDCJBDKIELABHIFLMN
       $.
 
     $( Bound-variable hypothesis builder for restricted uniqueness.
-       (Contributed by NM, 16-Jun-2017.) $)
+       (Contributed by NM, 16-Jun-2017.)  (New usage is discouraged.) $)
     nfrmo $p |- F/ x E* y e. A ph $=
       ( wrmo cv wcel wa wmo df-rmo wnf wtru nftru weq wal wn nfcvf a1i adantl
       wnfc nfeld nfand nfmod2 mptru nfxfr ) ACDGCHZDIZAJZCKZBACDLUKBMNUJBCCOBCP
@@ -30807,7 +30885,7 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     nfrab.2 $e |- F/_ x A $.
     $( A variable not free in a wff remains so in a restricted class
        abstraction.  (Contributed by NM, 13-Oct-2003.)  (Revised by Mario
-       Carneiro, 9-Oct-2016.) $)
+       Carneiro, 9-Oct-2016.)  (New usage is discouraged.) $)
     nfrab $p |- F/_ x { y e. A | ph } $=
       ( vz crab cv wcel wa cab df-rab wnfc wtru nftru weq wal wn wnf eleq1w a1i
       nfcri dvelimnf nfand adantl nfabd2 mptru nfcxfr ) BACDHCIDJZAKZCLZACDMBUL
@@ -31243,7 +31321,7 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     cbvralf.5 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Rule used to change bound variables, using implicit substitution.
        (Contributed by NM, 7-Mar-2004.)  (Revised by Mario Carneiro,
-       9-Oct-2016.) $)
+       9-Oct-2016.)  (New usage is discouraged.) $)
     cbvralf $p |- ( A. x e. A ph <-> A. y e. A ps ) $=
       ( vz cv wcel wi wal wral wsb nfv nfcri nfim nfs1v sbequ12 imbi12d cbvalv1
       weq eleq1w nfsb sbequ sbie syl6bb bitri df-ral 3bitr4i ) CLEMZANZCOZDLEMZ
@@ -31253,7 +31331,7 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
 
     $( Rule used to change bound variables, using implicit substitution.
        (Contributed by FL, 27-Apr-2008.)  (Revised by Mario Carneiro,
-       9-Oct-2016.) $)
+       9-Oct-2016.)  (New usage is discouraged.) $)
     cbvrexf $p |- ( E. x e. A ph <-> E. y e. A ps ) $=
       ( wn wral wrex nfn weq notbid cbvralf notbii dfrex2 3bitr4i ) AKZCELZKBKZ
       DELZKACEMBDEMUBUDUAUCCDEFGADHNBCINCDOABJPQRACESBDEST $.
@@ -31312,19 +31390,19 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     cbvral.2 $e |- F/ x ps $.
     cbvral.3 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 31-Jul-2003.) $)
+       (Contributed by NM, 31-Jul-2003.)  (New usage is discouraged.) $)
     cbvral $p |- ( A. x e. A ph <-> A. y e. A ps ) $=
       ( nfcv cbvralf ) ABCDECEIDEIFGHJ $.
 
     $( Rule used to change bound variables, using implicit substitution.
        (Contributed by NM, 31-Jul-2003.)  (Proof shortened by Andrew Salmon,
-       8-Jun-2011.) $)
+       8-Jun-2011.)  (New usage is discouraged.) $)
     cbvrex $p |- ( E. x e. A ph <-> E. y e. A ps ) $=
       ( nfcv cbvrexf ) ABCDECEIDEIFGHJ $.
 
     $( Change the bound variable of a restricted unique existential quantifier
        using implicit substitution.  (Contributed by Mario Carneiro,
-       15-Oct-2016.) $)
+       15-Oct-2016.)  (New usage is discouraged.) $)
     cbvreu $p |- ( E! x e. A ph <-> E! y e. A ps ) $=
       ( vz cv wcel wa weu wreu wsb nfv sb8eu sban eubii df-reu anbi1i nfsb nfan
       clelsb3 weq eleq1w sbequ sbie syl6bb anbi12d cbveu bitri 3bitri 3bitr4i )
@@ -31333,7 +31411,8 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
       VFURVCBIDEUFVHVCACDOBAIDCUGABCDGHUHUIUJUKULUMACETBDETUN $.
 
     $( Change the bound variable of a restricted at-most-one quantifier using
-       implicit substitution.  (Contributed by NM, 16-Jun-2017.) $)
+       implicit substitution.  (Contributed by NM, 16-Jun-2017.)
+       (New usage is discouraged.) $)
     cbvrmo $p |- ( E* x e. A ph <-> E* y e. A ps ) $=
       ( wrex wreu wi wrmo cbvrex cbvreu imbi12i rmo5 3bitr4i ) ACEIZACEJZKBDEIZ
       BDEJZKACELBDELRTSUAABCDEFGHMABCDEFGHNOACEPBDEPQ $.
@@ -31370,26 +31449,29 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     cbvralv.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Change the bound variable of a restricted universal quantifier using
        implicit substitution.  See ~ cbvralvw based on fewer axioms , but extra
-       disjoint variables.  (Contributed by NM, 28-Jan-1997.) $)
+       disjoint variables.  (Contributed by NM, 28-Jan-1997.)
+       (New usage is discouraged.) $)
     cbvralv $p |- ( A. x e. A ph <-> A. y e. A ps ) $=
       ( nfv cbvral ) ABCDEADGBCGFH $.
 
     $( Change the bound variable of a restricted existential quantifier using
        implicit substitution.  See ~ cbvrexvw based on fewer axioms , but extra
-       disjoint variables.  (Contributed by NM, 2-Jun-1998.) $)
+       disjoint variables.  (Contributed by NM, 2-Jun-1998.)
+       (New usage is discouraged.) $)
     cbvrexv $p |- ( E. x e. A ph <-> E. y e. A ps ) $=
       ( nfv cbvrex ) ABCDEADGBCGFH $.
 
     $( Change the bound variable of a restricted unique existential quantifier
        using implicit substitution.  See ~ cbvreuvw for a version without
        ~ ax-13 , but extra disjoint variables.  (Contributed by NM,
-       5-Apr-2004.)  (Revised by Mario Carneiro, 15-Oct-2016.) $)
+       5-Apr-2004.)  (Revised by Mario Carneiro, 15-Oct-2016.)
+       (New usage is discouraged.) $)
     cbvreuv $p |- ( E! x e. A ph <-> E! y e. A ps ) $=
       ( nfv cbvreu ) ABCDEADGBCGFH $.
 
     $( Change the bound variable of a restricted at-most-one quantifier using
        implicit substitution.  (Contributed by Alexander van der Vekens,
-       17-Jun-2017.) $)
+       17-Jun-2017.)  (New usage is discouraged.) $)
     cbvrmov $p |- ( E* x e. A ph <-> E* y e. A ps ) $=
       ( nfv cbvrmo ) ABCDEADGBCGFH $.
   $}
@@ -31493,7 +31575,8 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     cbvral2v.1 $e |- ( x = z -> ( ph <-> ch ) ) $.
     cbvral2v.2 $e |- ( y = w -> ( ch <-> ps ) ) $.
     $( Change bound variables of double restricted universal quantification,
-       using implicit substitution.  (Contributed by NM, 10-Aug-2004.) $)
+       using implicit substitution.  (Contributed by NM, 10-Aug-2004.)
+       (New usage is discouraged.) $)
     cbvral2v $p |- ( A. x e. A A. y e. B ph <-> A. z e. A A. w e. B ps ) $=
       ( wral weq ralbidv cbvralv ralbii bitri ) AEILZDHLCEILZFHLBGILZFHLRSDFHDF
       MACEIJNOSTFHCBEGIKOPQ $.
@@ -31505,7 +31588,8 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     cbvrex2v.1 $e |- ( x = z -> ( ph <-> ch ) ) $.
     cbvrex2v.2 $e |- ( y = w -> ( ch <-> ps ) ) $.
     $( Change bound variables of double restricted universal quantification,
-       using implicit substitution.  (Contributed by FL, 2-Jul-2012.) $)
+       using implicit substitution.  (Contributed by FL, 2-Jul-2012.)
+       (New usage is discouraged.) $)
     cbvrex2v $p |- ( E. x e. A E. y e. B ph <-> E. z e. A E. w e. B ps ) $=
       ( wrex weq rexbidv cbvrexv rexbii bitri ) AEILZDHLCEILZFHLBGILZFHLRSDFHDF
       MACEIJNOSTFHCBEGIKOPQ $.
@@ -31519,7 +31603,8 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     cbvral3v.2 $e |- ( y = v -> ( ch <-> th ) ) $.
     cbvral3v.3 $e |- ( z = u -> ( th <-> ps ) ) $.
     $( Change bound variables of triple restricted universal quantification,
-       using implicit substitution.  (Contributed by NM, 10-May-2005.) $)
+       using implicit substitution.  (Contributed by NM, 10-May-2005.)
+       (New usage is discouraged.) $)
     cbvral3v $p |- ( A. x e. A A. y e. B A. z e. C ph <->
                      A. w e. A A. v e. B A. u e. C ps ) $=
       ( wral weq 2ralbidv cbvralv cbvral2v ralbii bitri ) AGMQFLQZEKQCGMQFLQZHK
@@ -31549,7 +31634,8 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
   ${
     $d z x A $.  $d y A $.  $d z y ph $.
     $( Change bound variable by using a substitution.  (Contributed by NM,
-       20-Nov-2005.)  (Revised by Andrew Salmon, 11-Jul-2011.) $)
+       20-Nov-2005.)  (Revised by Andrew Salmon, 11-Jul-2011.)
+       (New usage is discouraged.) $)
     cbvralsv $p |- ( A. x e. A ph <-> A. y e. A [ y / x ] ph ) $=
       ( vz wral wsb nfv nfs1v sbequ12 cbvral nfsb sbequ bitri ) ABDFABEGZEDFABC
       GZCDFAOBEDAEHABEIABEJKOPECDABECACHLPEHAECBMKN $.
@@ -31558,7 +31644,8 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
   ${
     $d z x A $.  $d y z ph $.  $d y A $.
     $( Change bound variable by using a substitution.  (Contributed by NM,
-       2-Mar-2008.)  (Revised by Andrew Salmon, 11-Jul-2011.) $)
+       2-Mar-2008.)  (Revised by Andrew Salmon, 11-Jul-2011.)
+       (New usage is discouraged.) $)
     cbvrexsv $p |- ( E. x e. A ph <-> E. y e. A [ y / x ] ph ) $=
       ( vz wrex wsb nfv nfs1v sbequ12 cbvrex nfsb sbequ bitri ) ABDFABEGZEDFABC
       GZCDFAOBEDAEHABEIABEJKOPECDABECACHLPEHAECBMKN $.
@@ -31760,7 +31847,8 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     $( Rule to change the bound variable in a restricted class abstraction,
        using implicit substitution.  This version has bound-variable hypotheses
        in place of distinct variable conditions.  (Contributed by Andrew
-       Salmon, 11-Jul-2011.)  (Revised by Mario Carneiro, 9-Oct-2016.) $)
+       Salmon, 11-Jul-2011.)  (Revised by Mario Carneiro, 9-Oct-2016.)
+       (New usage is discouraged.) $)
     cbvrab $p |- { x e. A | ph } = { y e. A | ps } $=
       ( vz cv wcel wa cab crab wsb nfv nfcri nfan nfs1v weq eleq1w sbequ12 nfsb
       anbi12d cbvab sbequ sbie syl6bb eqtri df-rab 3eqtr4i ) CLEMZANZCOZDLEMZBN
@@ -34256,7 +34344,7 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     euxfr2.2 $e |- E* y x = A $.
     $( Transfer existential uniqueness from a variable ` x ` to another
        variable ` y ` contained in expression ` A ` .  (Contributed by NM,
-       14-Nov-2004.) $)
+       14-Nov-2004.)  (New usage is discouraged.) $)
     euxfr2 $p |- ( E! x E. y ( x = A /\ ph ) <-> E! y ph ) $=
       ( cv wceq wa wex weu wmo wi 2euswap moani ancom mobii mpbi mpg moeq biidd
       impbii ceqsexv eubii bitri ) BGDHZAIZCJBKZUGBJZCKZACKUHUJUGCLZUHUJMBUGBCN
@@ -34271,7 +34359,7 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     euxfr.3 $e |- ( x = A -> ( ph <-> ps ) ) $.
     $( Transfer existential uniqueness from a variable ` x ` to another
        variable ` y ` contained in expression ` A ` .  (Contributed by NM,
-       14-Nov-2004.) $)
+       14-Nov-2004.)  (New usage is discouraged.) $)
     euxfr $p |- ( E! x ph <-> E! y ps ) $=
       ( weu cv wceq wa wex euex ax-mp biantrur 19.41v pm5.32i exbii 3bitr2i
       eubii eumoi euxfr2 bitri ) ACICJEKZBLZDMZCIBDIAUGCAUEDMZALUEALZDMUGUHAUED
@@ -34874,12 +34962,12 @@ something like (wi (wceq (cv vx) (cv vy)) wph) ) into just (wcdeq vx vy
     ${
       $d x ps $.  $d y ph $.
       $( Distribute conditional equality over quantification.  (Contributed by
-         Mario Carneiro, 11-Aug-2016.) $)
+         Mario Carneiro, 11-Aug-2016.)  (New usage is discouraged.) $)
       cdeqal1 $p |- CondEq ( x = y -> ( A. x ph <-> A. y ps ) ) $=
         ( wal wb cdeqri cbvalv cdeqth ) ACFBDFGCDABCDABGCDEHIJ $.
 
       $( Distribute conditional equality over abstraction.  (Contributed by
-         Mario Carneiro, 11-Aug-2016.) $)
+         Mario Carneiro, 11-Aug-2016.)  (New usage is discouraged.) $)
       cdeqab1 $p |- CondEq ( x = y -> { x | ph } = { y | ps } ) $=
         ( cab wceq nfv wb cdeqri cbvab cdeqth ) ACFBDFGCDABCDADHBCHABICDEJKL $.
     $}
@@ -34919,7 +35007,8 @@ something like (wi (wceq (cv vx) (cv vy)) wph) ) into just (wcdeq vx vy
        and ` ps ` is ` ph ( y ) ` , and ` ph ( x ) ` in fact does not have
        ` x ` free in it according to ` F/ ` , then ` ph ( x ) <-> ph ( y ) `
        unconditionally.  This proves that ` F/ x ph ` is actually a not-free
-       predicate.  (Contributed by Mario Carneiro, 11-Aug-2016.) $)
+       predicate.  (Contributed by Mario Carneiro, 11-Aug-2016.)
+       (New usage is discouraged.) $)
     nfcdeq $p |- ( ph <-> ps ) $=
       ( wsb sbf nfv wb cdeqri sbie bitr3i ) AACDGBACDEHABCDBCIABJCDFKLM $.
   $}
@@ -34929,8 +35018,8 @@ something like (wi (wceq (cv vx) (cv vy)) wph) ) into just (wcdeq vx vy
     nfccdeq.1 $e |- F/_ x A $.
     nfccdeq.2 $e |- CondEq ( x = y -> A = B ) $.
     $( Variation of ~ nfcdeq for classes.  (Contributed by Mario Carneiro,
-       11-Aug-2016.)  Avoid ~ ax-11 .  (Revised by Gino Giotto,
-       19-May-2023.) $)
+       11-Aug-2016.)  Avoid ~ ax-11 .  (Revised by Gino Giotto, 19-May-2023.)
+       (New usage is discouraged.) $)
     nfccdeq $p |- A = B $=
       ( vz cv wcel nfcriv weq eqid cdeqth cdeqel nfcdeq eqriv ) GCDGHZCIQDIABAG
       CEJABQQCDGGKABQLMFNOP $.
@@ -35316,7 +35405,8 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     nfsbcd.2 $e |- ( ph -> F/_ x A ) $.
     nfsbcd.3 $e |- ( ph -> F/ x ps ) $.
     $( Deduction version of ~ nfsbc .  (Contributed by NM, 23-Nov-2005.)
-       (Revised by Mario Carneiro, 12-Oct-2016.) $)
+       (Revised by Mario Carneiro, 12-Oct-2016.)
+       (New usage is discouraged.) $)
     nfsbcd $p |- ( ph -> F/ x [. A / y ]. ps ) $=
       ( wsbc cab wcel df-sbc nfabd nfeld nfxfrd ) BDEIEBDJZKACBDELACEPGABCDFHMN
       O $.
@@ -35326,7 +35416,8 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     nfsbc.1 $e |- F/_ x A $.
     nfsbc.2 $e |- F/ x ph $.
     $( Bound-variable hypothesis builder for class substitution.  (Contributed
-       by NM, 7-Sep-2014.)  (Revised by Mario Carneiro, 12-Oct-2016.) $)
+       by NM, 7-Sep-2014.)  (Revised by Mario Carneiro, 12-Oct-2016.)
+       (New usage is discouraged.) $)
     nfsbc $p |- F/ x [. A / y ]. ph $=
       ( wsbc wnf wtru nftru wnfc a1i nfsbcd mptru ) ACDGBHIABCDCJBDKIELABHIFLMN
       $.
@@ -35335,7 +35426,8 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
   ${
     $d x z $.  $d z A $.  $d y z ph $.
     $( A composition law for class substitution.  (Contributed by NM,
-       26-Sep-2003.)  (Revised by Mario Carneiro, 13-Oct-2016.) $)
+       26-Sep-2003.)  (Revised by Mario Carneiro, 13-Oct-2016.)
+       (New usage is discouraged.) $)
     sbcco $p |- ( [. A / y ]. [. y / x ]. ph <-> [. A / x ]. ph ) $=
       ( vz cv wsbc cvv wcel sbcex dfsbcq wsb sbsbc sbbii sbco2 3bitr3ri vtoclbg
       nfv bitri pm5.21nii ) ABCFGZCDGZDHIABDGZUACDJABDJUACEFZGZABUDGZUBUCEDHUAC
@@ -35421,8 +35513,8 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     cbvsbc.2 $e |- F/ x ps $.
     cbvsbc.3 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Change bound variables in a wff substitution.  (Contributed by Jeff
-       Hankins, 19-Sep-2009.)  (Proof shortened by Andrew Salmon,
-       8-Jun-2011.) $)
+       Hankins, 19-Sep-2009.)  (Proof shortened by Andrew Salmon, 8-Jun-2011.)
+       (New usage is discouraged.) $)
     cbvsbc $p |- ( [. A / x ]. ph <-> [. A / y ]. ps ) $=
       ( cab wcel wsbc cbvab eleq2i df-sbc 3bitr4i ) EACIZJEBDIZJACEKBDEKPQEABCD
       FGHLMACENBDENO $.
@@ -35433,7 +35525,7 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     cbvsbcv.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Change the bound variable of a class substitution using implicit
        substitution.  (Contributed by NM, 30-Sep-2008.)  (Revised by Mario
-       Carneiro, 13-Oct-2016.) $)
+       Carneiro, 13-Oct-2016.)  (New usage is discouraged.) $)
     cbvsbcv $p |- ( [. A / x ]. ph <-> [. A / y ]. ps ) $=
       ( nfv cbvsbc ) ABCDEADGBCGFH $.
   $}
@@ -36315,7 +36407,7 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     $( Change bound variables in a class substitution.  Interestingly, this
        does not require any bound variable conditions on ` A ` .  (Contributed
        by Jeff Hankins, 13-Sep-2009.)  (Revised by Mario Carneiro,
-       11-Dec-2016.) $)
+       11-Dec-2016.)  (New usage is discouraged.) $)
     cbvcsb $p |- [_ A / x ]_ C = [_ A / y ]_ D $=
       ( vz cv wcel wsbc cab csb nfcri weq eleq2d cbvsbc abbii df-csb 3eqtr4i )
       IJZDKZACLZIMUBEKZBCLZIMACDNBCENUDUFIUCUEABCBIDFOAIEGOABPDEUBHQRSAICDTBICE
@@ -36360,7 +36452,7 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
   ${
     $d z A $.  $d y z B $.  $d x z $.
     $( Composition law for chained substitutions into a class.  (Contributed by
-       NM, 10-Nov-2005.) $)
+       NM, 10-Nov-2005.)  (New usage is discouraged.) $)
     csbco $p |- [_ A / y ]_ [_ y / x ]_ B = [_ A / x ]_ B $=
       ( vz cv csb wcel wsbc cab df-csb abeq2i sbcbii sbcco bitri abbii 3eqtr4i
       ) EFZABFZDGZHZBCIZEJRDHZACIZEJBCTGACDGUBUDEUBUCASIZBCIUDUAUEBCUEETAESDKLM
@@ -36448,7 +36540,8 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     nfcsbd.2 $e |- ( ph -> F/_ x A ) $.
     nfcsbd.3 $e |- ( ph -> F/_ x B ) $.
     $( Deduction version of ~ nfcsb .  (Contributed by NM, 21-Nov-2005.)
-       (Revised by Mario Carneiro, 12-Oct-2016.) $)
+       (Revised by Mario Carneiro, 12-Oct-2016.)
+       (New usage is discouraged.) $)
     nfcsbd $p |- ( ph -> F/_ x [_ A / y ]_ B ) $=
       ( vz csb cv wcel wsbc cab df-csb nfv nfcrd nfsbcd nfabd nfcxfrd ) ABCDEJI
       KELZCDMZINCIDEOAUBBIAIPAUABCDFGABIEHQRST $.
@@ -36471,7 +36564,8 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     nfcsb.1 $e |- F/_ x A $.
     nfcsb.2 $e |- F/_ x B $.
     $( Bound-variable hypothesis builder for substitution into a class.
-       (Contributed by Mario Carneiro, 12-Oct-2016.) $)
+       (Contributed by Mario Carneiro, 12-Oct-2016.)
+       (New usage is discouraged.) $)
     nfcsb $p |- F/_ x [_ A / y ]_ B $=
       ( csb wnfc wtru nftru a1i nfcsbd mptru ) ABCDGHIABCDBJACHIEKADHIFKLM $.
   $}
@@ -36665,7 +36759,8 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     cbvralcsf.6 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( A more general version of ~ cbvralf that doesn't require ` A ` and ` B `
        to be distinct from ` x ` or ` y ` .  Changes bound variables using
-       implicit substitution.  (Contributed by Andrew Salmon, 13-Jul-2011.) $)
+       implicit substitution.  (Contributed by Andrew Salmon, 13-Jul-2011.)
+       (New usage is discouraged.) $)
     cbvralcsf $p |- ( A. x e. A ph <-> A. y e. B ps ) $=
       ( vz vv cv wcel wi wal wsbc nfcri wral csb nfv nfcsb1v nfsbc1v id csbeq1a
       nfim weq eleq12d sbceq1a imbi12d cbvalv1 nfcv nfcsb csbeq1 cab df-csb wsb
@@ -36680,14 +36775,15 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     $( A more general version of ~ cbvrexf that has no distinct variable
        restrictions.  Changes bound variables using implicit substitution.
        (Contributed by Andrew Salmon, 13-Jul-2011.)  (Proof shortened by Mario
-       Carneiro, 7-Dec-2014.) $)
+       Carneiro, 7-Dec-2014.)  (New usage is discouraged.) $)
     cbvrexcsf $p |- ( E. x e. A ph <-> E. y e. B ps ) $=
       ( wn wral wrex nfn weq notbid cbvralcsf dfrex2 notbii 3bitr4i ) AMZCENZMB
       MZDFNZMACEOBDFOUDUFUCUECDEFGHADIPBCJPKCDQABLRSUAACETBDFTUB $.
 
     $( A more general version of ~ cbvreuv that has no distinct variable
        restrictions.  Changes bound variables using implicit substitution.
-       (Contributed by Andrew Salmon, 13-Jul-2011.) $)
+       (Contributed by Andrew Salmon, 13-Jul-2011.)
+       (New usage is discouraged.) $)
     cbvreucsf $p |- ( E! x e. A ph <-> E! y e. B ps ) $=
       ( vz vv cv wcel wa weu wsb nfcri wreu csb nfv nfcsb1v nfan weq id csbeq1a
       nfs1v eleq12d sbequ12 anbi12d cbveu nfcv nfcsb nfsb csbeq1 cab wsbc sbsbc
@@ -36700,7 +36796,8 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
       EVLBDFVLVM $.
 
     $( A more general version of ~ cbvrab with no distinct variable
-       restrictions.  (Contributed by Andrew Salmon, 13-Jul-2011.) $)
+       restrictions.  (Contributed by Andrew Salmon, 13-Jul-2011.)
+       (New usage is discouraged.) $)
     cbvrabcsf $p |- { x e. A | ph } = { y e. B | ps } $=
       ( vz vv cv wcel wa cab wsb nfcri crab csb nfv nfcsb1v nfan weq id csbeq1a
       nfs1v eleq12d sbequ12 anbi12d cbvab nfcv nfcsb csbeq1 df-csb eleq2d sbsbc
@@ -36718,13 +36815,15 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     cbvralv2.2 $e |- ( x = y -> A = B ) $.
     $( Rule used to change the bound variable in a restricted universal
        quantifier with implicit substitution which also changes the quantifier
-       domain.  (Contributed by David Moews, 1-May-2017.) $)
+       domain.  (Contributed by David Moews, 1-May-2017.)
+       (New usage is discouraged.) $)
     cbvralv2 $p |- ( A. x e. A ps <-> A. y e. B ch ) $=
       ( nfcv nfv cbvralcsf ) ABCDEFDEICFIADJBCJHGK $.
 
     $( Rule used to change the bound variable in a restricted existential
        quantifier with implicit substitution which also changes the quantifier
-       domain.  (Contributed by David Moews, 1-May-2017.) $)
+       domain.  (Contributed by David Moews, 1-May-2017.)
+       (New usage is discouraged.) $)
     cbvrexv2 $p |- ( E. x e. A ps <-> E. y e. B ch ) $=
       ( nfcv nfv cbvrexcsf ) ABCDEFDEICFIADJBCJHGK $.
   $}
@@ -40269,7 +40368,7 @@ among classes ( ~ eq0 , as opposed to the weaker uniqueness among sets,
   ${
     $d x z $.  $d y z $.  $d z A $.  $d z B $.  $d z C $.  $d z ph $.
     $( Nest the composition of two substitutions.  (Contributed by Mario
-       Carneiro, 11-Nov-2016.) $)
+       Carneiro, 11-Nov-2016.)  (New usage is discouraged.) $)
     sbcnestgf $p |- ( ( A e. V /\ A. y F/ x ph ) ->
          ( [. A / x ]. [. B / y ]. ph <-> [. [_ A / x ]_ B / y ]. ph ) ) $=
       ( vz wcel wnf wal wsbc csb wb cv wi wceq dfsbcq sbceq1d cvv a1i vex nfnf1
@@ -40280,7 +40379,8 @@ among classes ( ~ eq0 , as opposed to the weaker uniqueness among sets,
       OUMUP $.
 
     $( Nest the composition of two substitutions.  (Contributed by NM,
-       23-Nov-2005.)  (Proof shortened by Mario Carneiro, 10-Nov-2016.) $)
+       23-Nov-2005.)  (Proof shortened by Mario Carneiro, 10-Nov-2016.)
+       (New usage is discouraged.) $)
     csbnestgf $p |- ( ( A e. V /\ A. y F/_ x C ) ->
          [_ A / x ]_ [_ B / y ]_ C = [_ [_ A / x ]_ B / y ]_ C ) $=
       ( vz wcel wnfc wal wa cv csb wsbc cab cvv wceq elex df-csb abeq2i wb nfcr
@@ -40291,7 +40391,8 @@ among classes ( ~ eq0 , as opposed to the weaker uniqueness among sets,
 
     $d x ph $.
     $( Nest the composition of two substitutions.  (Contributed by NM,
-       27-Nov-2005.)  (Proof shortened by Mario Carneiro, 11-Nov-2016.) $)
+       27-Nov-2005.)  (Proof shortened by Mario Carneiro, 11-Nov-2016.)
+       (New usage is discouraged.) $)
     sbcnestg $p |- ( A e. V ->
           ( [. A / x ]. [. B / y ]. ph <-> [. [_ A / x ]_ B / y ]. ph ) ) $=
       ( wcel wnf wal wsbc csb wb nfv ax-gen sbcnestgf mpan2 ) DFGABHZCIACEJBDJA
@@ -40299,7 +40400,8 @@ among classes ( ~ eq0 , as opposed to the weaker uniqueness among sets,
 
     $d x C $.
     $( Nest the composition of two substitutions.  (Contributed by NM,
-       23-Nov-2005.)  (Proof shortened by Mario Carneiro, 10-Nov-2016.) $)
+       23-Nov-2005.)  (Proof shortened by Mario Carneiro, 10-Nov-2016.)
+       (New usage is discouraged.) $)
     csbnestg $p |- ( A e. V ->
           [_ A / x ]_ [_ B / y ]_ C = [_ [_ A / x ]_ B / y ]_ C ) $=
       ( wcel wnfc wal csb wceq nfcv ax-gen csbnestgf mpan2 ) CFGAEHZBIACBDEJJBA
@@ -40310,7 +40412,8 @@ among classes ( ~ eq0 , as opposed to the weaker uniqueness among sets,
     $d x A $.  $d x ph $.  $d x C $.  $d x D $.
     sbcco3g.1 $e |- ( x = A -> B = C ) $.
     $( Composition of two substitutions.  (Contributed by NM, 27-Nov-2005.)
-       (Revised by Mario Carneiro, 11-Nov-2016.) $)
+       (Revised by Mario Carneiro, 11-Nov-2016.)
+       (New usage is discouraged.) $)
     sbcco3g $p |- ( A e. V ->
          ( [. A / x ]. [. B / y ]. ph <-> [. C / y ]. ph ) ) $=
       ( wcel wsbc csb sbcnestg cvv wceq wb elex nfcvd csbiegf dfsbcq 3syl bitrd
@@ -40318,7 +40421,8 @@ among classes ( ~ eq0 , as opposed to the weaker uniqueness among sets,
       $.
 
     $( Composition of two class substitutions.  (Contributed by NM,
-       27-Nov-2005.)  (Revised by Mario Carneiro, 11-Nov-2016.) $)
+       27-Nov-2005.)  (Revised by Mario Carneiro, 11-Nov-2016.)
+       (New usage is discouraged.) $)
     csbco3g $p |- ( A e. V ->
                  [_ A / x ]_ [_ B / y ]_ D = [_ C / y ]_ D ) $=
       ( wcel csb csbnestg cvv wceq elex nfcvd csbiegf syl csbeq1d eqtrd ) CGIZA
@@ -45513,14 +45617,16 @@ same distinct variable group (meaning ` A ` cannot depend on ` x ` ) and
     nfiung.2 $e |- F/_ y B $.
     $( Bound-variable hypothesis builder for indexed union.  See ~ nfiun for a
        version with more disjoint variable conditions, but not requiring
-       ~ ax-13 .  (Contributed by Mario Carneiro, 25-Jan-2014.) $)
+       ~ ax-13 .  (Contributed by Mario Carneiro, 25-Jan-2014.)
+       (New usage is discouraged.) $)
     nfiung $p |- F/_ y U_ x e. A B $=
       ( vz ciun cv wcel wrex cab df-iun nfcri nfrexg nfabg nfcxfr ) BACDHGIDJZA
       CKZGLAGCDMSBGRBACEBGDFNOPQ $.
 
     $( Bound-variable hypothesis builder for indexed intersection.  See ~ nfiin
        for a version with more disjoint variable conditions, but not requiring
-       ~ ax-13 .  (Contributed by Mario Carneiro, 25-Jan-2014.) $)
+       ~ ax-13 .  (Contributed by Mario Carneiro, 25-Jan-2014.)
+       (New usage is discouraged.) $)
     nfiing $p |- F/_ y |^|_ x e. A B $=
       ( vz ciin cv wcel wral cab df-iin nfcri nfral nfabg nfcxfr ) BACDHGIDJZAC
       KZGLAGCDMSBGRBACEBGDFNOPQ $.
@@ -45650,7 +45756,7 @@ same distinct variable group (meaning ` A ` cannot depend on ` x ` ) and
        substitution specified implicitly by the hypothesis.  See ~ cbviun for a
        version with more disjoint variable conditions, but not requiring
        ~ ax-13 .  (Contributed by NM, 26-Mar-2006.)  (Revised by Andrew Salmon,
-       25-Jul-2011.) $)
+       25-Jul-2011.)  (New usage is discouraged.) $)
     cbviung $p |- U_ x e. A B = U_ y e. A C $=
       ( vz cv wcel wrex cab ciun nfcri weq eleq2d cbvrex abbii df-iun 3eqtr4i )
       IJZDKZACLZIMUBEKZBCLZIMACDNBCENUDUFIUCUEABCBIDFOAIEGOABPDEUBHQRSAICDTBICE
@@ -45659,7 +45765,7 @@ same distinct variable group (meaning ` A ` cannot depend on ` x ` ) and
     $( Change bound variables in an indexed intersection.  See ~ cbviin for a
        version with more disjoint variable conditions, but not requiring
        ~ ax-13 .  (Contributed by Jeff Hankins, 26-Aug-2009.)  (Revised by
-       Mario Carneiro, 14-Oct-2016.) $)
+       Mario Carneiro, 14-Oct-2016.)  (New usage is discouraged.) $)
     cbviing $p |- |^|_ x e. A B = |^|_ y e. A C $=
       ( vz cv wcel wral cab ciin nfcri weq eleq2d cbvral abbii df-iin 3eqtr4i )
       IJZDKZACLZIMUBEKZBCLZIMACDNBCENUDUFIUCUEABCBIDFOAIEGOABPDEUBHQRSAICDTBICE
@@ -45692,12 +45798,12 @@ same distinct variable group (meaning ` A ` cannot depend on ` x ` ) and
     cbviunvg.1 $e |- ( x = y -> B = C ) $.
     $( Rule used to change the bound variables in an indexed union, with the
        substitution specified implicitly by the hypothesis.  (Contributed by
-       NM, 15-Sep-2003.) $)
+       NM, 15-Sep-2003.)  (New usage is discouraged.) $)
     cbviunvg $p |- U_ x e. A B = U_ y e. A C $=
       ( nfcv cbviung ) ABCDEBDGAEGFH $.
 
     $( Change bound variables in an indexed intersection.  (Contributed by Jeff
-       Hankins, 26-Aug-2009.) $)
+       Hankins, 26-Aug-2009.)  (New usage is discouraged.) $)
     cbviinvg $p |- |^|_ x e. A B = |^|_ y e. A C $=
       ( nfcv cbviing ) ABCDEBDGAEGFH $.
   $}
@@ -46421,7 +46527,7 @@ same distinct variable group (meaning ` A ` cannot depend on ` x ` ) and
     nfdisj.1 $e |- F/_ y A $.
     nfdisj.2 $e |- F/_ y B $.
     $( Bound-variable hypothesis builder for disjoint collection.  (Contributed
-       by Mario Carneiro, 14-Nov-2016.) $)
+       by Mario Carneiro, 14-Nov-2016.)  (New usage is discouraged.) $)
     nfdisj $p |- F/ y Disj_ x e. A B $=
       ( vz wdisj cv wcel wa wmo wal dfdisj2 wnf wtru nftru weq wn a1i wnfc nfal
       nfcvf nfeld nfcri nfand adantl nfmod2 mptru nfxfr ) ACDHAIZCJZGIDJZKZALZG
@@ -46717,7 +46823,7 @@ same distinct variable group (meaning ` A ` cannot depend on ` x ` ) and
     $d w x y z A $.  $d w x y z B $.  $d w y z C $.  $d w x z D $.
     disjxun.1 $e |- ( x = y -> C = D ) $.
     $( The union of two disjoint collections.  (Contributed by Mario Carneiro,
-       14-Nov-2016.) $)
+       14-Nov-2016.)  (New usage is discouraged.) $)
     disjxun $p |- ( ( A i^i B ) = (/) -> ( Disj_ x e. ( A u. B ) C <->
       ( Disj_ x e. A C /\ Disj_ x e. B C /\
         A. x e. A A. y e. B ( C i^i D ) = (/) ) ) ) $=
@@ -47431,7 +47537,8 @@ although the definition does not require it (see ~ dfid2 for a case
     $( Change first bound variable in an ordered-pair class abstraction, using
        explicit substitution.  See ~ cbvopab1 for a version with more disjoint
        variable conditions, but not requiring ~ ax-13 .  (Contributed by NM,
-       6-Oct-2004.)  (Revised by Mario Carneiro, 14-Oct-2016.) $)
+       6-Oct-2004.)  (Revised by Mario Carneiro, 14-Oct-2016.)
+       (New usage is discouraged.) $)
     cbvopab1g $p |- { <. x , y >. | ph } = { <. z , y >. | ps } $=
       ( vw vv cv cop wceq wa wex cab copab wsb nfv nfan nfs1v nfex opeq1 eqeq2d
       sbequ12 anbi12d exbidv cbvexv1 nfsb sbequ sbie syl6bb bitri abbii df-opab
@@ -47723,7 +47830,8 @@ although the definition does not require it (see ~ dfid2 for a case
        substitution.  This version has bound-variable hypotheses in place of
        distinct variable conditions.  See ~ cbvmptf for a version with more
        disjoint variable conditions, but not requiring ~ ax-13 .  (Contributed
-       by NM, 11-Sep-2011.)  (Revised by Thierry Arnoux, 9-Mar-2017.) $)
+       by NM, 11-Sep-2011.)  (Revised by Thierry Arnoux, 9-Mar-2017.)
+       (New usage is discouraged.) $)
     cbvmptfg $p |- ( x e. A |-> B ) = ( y e. A |-> C ) $=
       ( vz vw cv wcel wceq wa copab cmpt wsb weq nfv nfcri nfs1v eleq1w sbequ12
       nfan anbi12d cbvopab1g nfeq2 nfsb sbequ eqeq2d sbie syl6bb df-mpt 3eqtr4i
@@ -47758,7 +47866,7 @@ although the definition does not require it (see ~ dfid2 for a case
        substitution.  This version has bound-variable hypotheses in place of
        distinct variable conditions.  See ~ cbvmpt for a version with more
        disjoint variable conditions, but not requiring ~ ax-13 .  (Contributed
-       by NM, 11-Sep-2011.) $)
+       by NM, 11-Sep-2011.)  (New usage is discouraged.) $)
     cbvmptg $p |- ( x e. A |-> B ) = ( y e. A |-> C ) $=
       ( nfcv cbvmptfg ) ABCDEACIBCIFGHJ $.
   $}
@@ -47782,7 +47890,7 @@ although the definition does not require it (see ~ dfid2 for a case
     $( Rule to change the bound variable in a maps-to function, using implicit
        substitution.  See ~ cbvmptv for a version with more disjoint variable
        conditions, but not requiring ~ ax-13 .  (Contributed by Mario Carneiro,
-       19-Feb-2013.) $)
+       19-Feb-2013.)  (New usage is discouraged.) $)
     cbvmptvg $p |- ( x e. A |-> B ) = ( y e. A |-> C ) $=
       ( nfcv cbvmptg ) ABCDEBDGAEGFH $.
   $}
@@ -48933,7 +49041,7 @@ This theorem is proved directly from set theory axioms (no set theory
     dtrucor2.1 $e |- ( x = y -> x =/= y ) $.
     $( The theorem form of the deduction ~ dtrucor leads to a contradiction, as
        mentioned in the "Wrong!" example at ~ mmdeduction.html#bad .
-       (Contributed by NM, 20-Oct-2007.) $)
+       (Contributed by NM, 20-Oct-2007.)  (New usage is discouraged.) $)
     dtrucor2 $p |- ( ph /\ -. ph ) $=
       ( weq wex wn wa ax6e wi cv necon2bi pm2.01 ax-mp nex pm2.24ii ) BCEZBFAAG
       HBCIQBQQGZJRQBKCKDLQMNOP $.
@@ -49012,7 +49120,7 @@ That theorem bundles the theorems ( ` |- E. x ( x = y -> z e. x ) ` with
      ` y ` are not the same variable, can be written in terms of ` F/ ` in the
      obvious way.  This theorem is not true in a one-element domain, because
      then ` F/_ x y ` and ` A. x x = y ` will both be true.  (Contributed by
-     Mario Carneiro, 8-Oct-2016.) $)
+     Mario Carneiro, 8-Oct-2016.)  (New usage is discouraged.) $)
   nfcvb $p |- ( F/_ x y <-> -. A. x x = y ) $=
     ( cv wnfc weq wal wn nfnid eqidd drnfc1 mtbiri con2i nfcvf impbii ) ABCZDZA
     BEAFZGQPQPBODBHABOOQOIJKLABMN $.
@@ -50172,7 +50280,8 @@ That theorem bundles the theorems ( ` |- E. x ( x = y -> z e. x ) ` with
     $d x z w A $.  $d y z w A $.  $d z w ph $.
     $( Substitution of class ` A ` for ordered pair ` <. x , y >. ` .
        (Contributed by NM, 27-Dec-1996.)  (Revised by Andrew Salmon,
-       11-Jul-2011.)  (Proof shortened by Wolf Lammen, 25-Aug-2019.) $)
+       11-Jul-2011.)  (Proof shortened by Wolf Lammen, 25-Aug-2019.)
+       (New usage is discouraged.) $)
     copsexg $p |- ( A = <. x , y >. ->
                   ( ph <-> E. x E. y ( A = <. x , y >. /\ ph ) ) ) $=
       ( vz vw cv cop wceq wa wex wb wi vex 19.8a weq syl5 syl5bi weu euequ opth
@@ -50671,7 +50780,7 @@ necessary if all involved classes exist as sets (i.e. are not proper
     $d x z $.  $d y z $.  $d ph z $.
     $( The law of concretion.  Special case of Theorem 9.5 of [Quine] p. 61.
        (Contributed by NM, 14-Apr-1995.)  (Proof shortened by Andrew Salmon,
-       25-Jul-2011.) $)
+       25-Jul-2011.)  (New usage is discouraged.) $)
     opabid $p |- ( <. x , y >. e. { <. x , y >. | ph } <-> ph ) $=
       ( vz cv cop wceq wa wex copab opex copsexg bicomd df-opab elab2 ) DEZBEZC
       EZFZGZAHCIBIZADSABCJQRKTAUAABCPLMABCDNO $.
@@ -50943,7 +51052,7 @@ necessary if all involved classes exist as sets (i.e. are not proper
 
   $( Equivalence of ordered pair abstraction subclass and implication.
      (Contributed by NM, 27-Dec-1996.)  (Proof shortened by Mario Carneiro,
-     18-Nov-2016.) $)
+     18-Nov-2016.)  (New usage is discouraged.) $)
   ssopab2b $p |- ( { <. x , y >. | ph } C_ { <. x , y >. | ps } <->
                A. x A. y ( ph -> ps ) ) $=
     ( copab wss wi wal nfopab1 nfss nfopab2 cop wcel ssel opabid 3imtr3g alrimi
@@ -50970,7 +51079,8 @@ necessary if all involved classes exist as sets (i.e. are not proper
   $}
 
   $( Equivalence of ordered pair abstraction equality and biconditional.
-     (Contributed by Mario Carneiro, 4-Jan-2017.) $)
+     (Contributed by Mario Carneiro, 4-Jan-2017.)
+     (New usage is discouraged.) $)
   eqopab2b $p |- ( { <. x , y >. | ph } = { <. x , y >. | ps }
                 <-> A. x A. y ( ph <-> ps ) ) $=
     ( copab wss wa wi wal wceq wb ssopab2b anbi12i eqss 2albiim 3bitr4i ) ACDEZ
@@ -55425,10 +55535,10 @@ the restriction (of the relation) to the singleton containing this
        ` A ` is empty.  (Contributed by AV, 30-Jan-2024.) $)
     iresn0n0 $p |- ( A = (/) <-> ( _I |` A ) = (/) ) $=
       ( vx vy cv wcel weq wa copab c0 wceq wal cid opab0 opabresid eqeq1i nel02
-      wn cres wo sylbi intnanrd alrimivv ianor albii 19.32v id ax6 pm2.21i jaoi
-      alimi eq0 sylibr impbii 3bitr4ri ) BDZAEZCBFZGZBCHZIJURQZCKZBKZLARZIJAIJZ
-      URBCMVCUSIBCANOVDVBVDUTBCVDUPUQAUOPUAUBVBUPQZBKVDVAVEBVAVEUQQZSZCKZVEUTVG
-      CUPUQUCUDVHVEVFCKZSVEVEVFCUEVEVEVIVEUFVIVECBUGUHUITTUJBAUKULUMUN $.
+      wn cres wo sylbi intnanrd alrimivv ianor albii id ax6v pm2.21i jaoi alimi
+      19.32v eq0 sylibr impbii 3bitr4ri ) BDZAEZCBFZGZBCHZIJURQZCKZBKZLARZIJAIJ
+      ZURBCMVCUSIBCANOVDVBVDUTBCVDUPUQAUOPUAUBVBUPQZBKVDVAVEBVAVEUQQZSZCKZVEUTV
+      GCUPUQUCUDVHVEVFCKZSVEVEVFCUJVEVEVIVEUEVIVECBUFUGUHTTUIBAUKULUMUN $.
   $}
 
   $( Equality theorem for image.  (Contributed by NM, 14-Aug-1994.) $)
@@ -58878,7 +58988,8 @@ Definite description binder (inverted iota)
     $d z ps $.  $d z ph $.  $d x z $.  $d y z $.
     nfiotad.1 $e |- F/ y ph $.
     nfiotad.2 $e |- ( ph -> F/ x ps ) $.
-    $( Deduction version of ~ nfiota .  (Contributed by NM, 18-Feb-2013.) $)
+    $( Deduction version of ~ nfiota .  (Contributed by NM, 18-Feb-2013.)
+       (New usage is discouraged.) $)
     nfiotad $p |- ( ph -> F/_ x ( iota y ps ) ) $=
       ( vz cio weq wb wal cab cuni dfiota2 nfv wn wa wnf adantr nfeqf1 nfcxfrd
       adantl nfbid nfald2 nfabd nfunid ) ACBDHBDGIZJZDKZGLZMBDGNACUJAUICGAGOAUH
@@ -58888,7 +58999,7 @@ Definite description binder (inverted iota)
   ${
     nfiota.1 $e |- F/ x ph $.
     $( Bound-variable hypothesis builder for the ` iota ` class.  (Contributed
-       by NM, 23-Aug-2011.) $)
+       by NM, 23-Aug-2011.)  (New usage is discouraged.) $)
     nfiota $p |- F/_ x ( iota y ph ) $=
       ( cio wnfc wtru nftru wnf a1i nfiotad mptru ) BACEFGABCCHABIGDJKL $.
   $}
@@ -58925,7 +59036,7 @@ Definite description binder (inverted iota)
     cbviota.2 $e |- F/ y ph $.
     cbviota.3 $e |- F/ x ps $.
     $( Change bound variables in a description binder.  (Contributed by Andrew
-       Salmon, 1-Aug-2011.) $)
+       Salmon, 1-Aug-2011.)  (New usage is discouraged.) $)
     cbviota $p |- ( iota x ph ) = ( iota y ps ) $=
       ( vw vz weq wb wal cab cuni cio wsb nfv nfbi equequ1 bibi12d sbequ12 nfsb
       nfs1v cbvalv1 sbequ sbie syl6bb bitri abbii unieqi dfiota2 3eqtr4i ) ACHJ
@@ -58938,7 +59049,7 @@ Definite description binder (inverted iota)
     $d ph y $.  $d ps x $.
     cbviotav.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Change bound variables in a description binder.  (Contributed by Andrew
-       Salmon, 1-Aug-2011.) $)
+       Salmon, 1-Aug-2011.)  (New usage is discouraged.) $)
     cbviotav $p |- ( iota x ph ) = ( iota y ps ) $=
       ( nfv cbviota ) ABCDEADFBCFG $.
   $}
@@ -58947,7 +59058,7 @@ Definite description binder (inverted iota)
     $d w z ph $.  $d w z x $.  $d w z y $.
     sb8iota.1 $e |- F/ y ph $.
     $( Variable substitution in description binder.  Compare ~ sb8eu .
-       (Contributed by NM, 18-Mar-2013.) $)
+       (Contributed by NM, 18-Mar-2013.)  (New usage is discouraged.) $)
     sb8iota $p |- ( iota x ph ) = ( iota y [ y / x ] ph ) $=
       ( vz vw weq wal cab cuni wsb cio nfv sb8 sbbi nfsb equsb3 nfxfr dfiota2
       wb nfbi sbequ cbvalv1 sblbis albii 3bitri abbii unieqi 3eqtr4i ) ABEGZTZB
@@ -58959,7 +59070,7 @@ Definite description binder (inverted iota)
   ${
     $d y z $.  $d x z $.  $d ph z $.
     $( Equality theorem for descriptions.  (Contributed by Andrew Salmon,
-       30-Jun-2011.) $)
+       30-Jun-2011.)  (New usage is discouraged.) $)
     iotaeq $p |- ( A. x x = y -> ( iota x ph ) = ( iota y ph ) ) $=
       ( vz cv wceq wal cab csn cuni cio wcel drsb1 df-clab 3bitr4g eqrdv eqeq1d
       wsb abbidv df-iota unieqd 3eqtr4g ) BECEFBGZABHZDEZIZFZDHZJACHZUFFZDHZJAB
@@ -63229,7 +63340,8 @@ empty set when it is not meaningful (as shown by ~ ndmfv and ~ fvprc ).
     $( Implications for the value of a function defined by the maps-to notation
        with a class abstraction as a result having an element.  Here, the base
        set of the class abstraction depends on the argument of the function.
-       (Contributed by Alexander van der Vekens, 15-Jul-2018.) $)
+       (Contributed by Alexander van der Vekens, 15-Jul-2018.)
+       (New usage is discouraged.) $)
     elfvmptrab1 $p |- ( Y e. ( F ` X )
                         -> ( X e. V /\ Y e. [_ X / m ]_ M ) ) $=
       ( cfv wcel csb c0 crab cvv wceq 3syl nfcv wa wne ne0i ndmfv necon1ai wsbc
@@ -63984,7 +64096,7 @@ in the range of the function (the implication "to the right" is always
     ralrnmpt.1 $e |- F = ( x e. A |-> B ) $.
     ralrnmpt.2 $e |- ( y = B -> ( ps <-> ch ) ) $.
     $( A restricted quantifier over an image set.  (Contributed by Mario
-       Carneiro, 20-Aug-2015.) $)
+       Carneiro, 20-Aug-2015.)  (New usage is discouraged.) $)
     ralrnmpt $p |- ( A. x e. A B e. V ->
       ( A. y e. ran F ps <-> A. x e. A ch ) ) $=
       ( vw vz wcel wral cv cfv wsbc wb syl nfv crn fnmpt dfsbcq nfsbc1v sbceq1a
@@ -63996,7 +64108,7 @@ in the range of the function (the implication "to the right" is always
       TZVMADFQZBWEADVLFCEFHGIVAUPVGWFBRWDABDFHJVBVCVDVEVMBCEVFSVD $.
 
     $( A restricted quantifier over an image set.  (Contributed by Mario
-       Carneiro, 20-Aug-2015.) $)
+       Carneiro, 20-Aug-2015.)  (New usage is discouraged.) $)
     rexrnmpt $p |- ( A. x e. A B e. V ->
       ( E. y e. ran F ps <-> E. x e. A ch ) ) $=
       ( wcel wral wn crn wrex cv wceq notbid ralrnmpt dfrex2 3bitr4g ) FHKCELZA
@@ -67428,7 +67540,8 @@ Restricted iota (description binder)
     nfriotad.2 $e |- ( ph -> F/ x ps ) $.
     nfriotad.3 $e |- ( ph -> F/_ x A ) $.
     $( Deduction version of ~ nfriota .  (Contributed by NM, 18-Feb-2013.)
-       (Revised by Mario Carneiro, 15-Oct-2016.) $)
+       (Revised by Mario Carneiro, 15-Oct-2016.)
+       (New usage is discouraged.) $)
     nfriotad $p |- ( ph -> F/_ x ( iota_ y e. A ps ) ) $=
       ( crio cv wcel wa cio df-riota weq wal wnfc wn nfnae adantr nfcvf nfiotad
       nfan adantl nfeld wnf nfand nfiota1 eqidd drnfc1 mpbiri pm2.61d2 nfcxfrd
@@ -67454,7 +67567,8 @@ Restricted iota (description binder)
     cbvriota.2 $e |- F/ x ps $.
     cbvriota.3 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Change bound variable in a restricted description binder.  (Contributed
-       by NM, 18-Mar-2013.)  (Revised by Mario Carneiro, 15-Oct-2016.) $)
+       by NM, 18-Mar-2013.)  (Revised by Mario Carneiro, 15-Oct-2016.)
+       (New usage is discouraged.) $)
     cbvriota $p |- ( iota_ x e. A ph ) = ( iota_ y e. A ps ) $=
       ( vz cv wcel wa cio crio wsb weq eleq1w anbi12d nfv nfan nfs1v sbequ sbie
       sbequ12 cbviota syl6bb nfsb eqtri df-riota 3eqtr4i ) CJEKZALZCMZDJEKZBLZD
@@ -67467,7 +67581,8 @@ Restricted iota (description binder)
     $d x A $.  $d y A $.  $d y ph $.  $d x ps $.
     cbvriotav.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Change bound variable in a restricted description binder.  (Contributed
-       by NM, 18-Mar-2013.)  (Revised by Mario Carneiro, 15-Oct-2016.) $)
+       by NM, 18-Mar-2013.)  (Revised by Mario Carneiro, 15-Oct-2016.)
+       (New usage is discouraged.) $)
     cbvriotav $p |- ( iota_ x e. A ph ) = ( iota_ y e. A ps ) $=
       ( nfv cbvriota ) ABCDEADGBCGFH $.
   $}
@@ -68088,7 +68203,8 @@ ordered pairs (for use in defining operations).  This is a special case
   ${
     $d a ph r s t w $.  $d a r s t w x $.  $d a r s t w y $.  $d a r s t w z $.
     $( The law of concretion.  Special case of Theorem 9.5 of [Quine] p. 61.
-       (Contributed by Mario Carneiro, 20-Mar-2013.) $)
+       (Contributed by Mario Carneiro, 20-Mar-2013.)
+       (New usage is discouraged.) $)
     oprabid $p |- ( <. <. x , y >. , z >. e.
         { <. <. x , y >. , z >. | ph } <-> ph ) $=
       ( vw va vt vr vs cv cop wceq wa wex wi vex weq weu euequ eupick eqeq1 w3a
@@ -68475,7 +68591,7 @@ ordered pairs (for use in defining operations).  This is a special case
 
   $( Equivalence of ordered pair abstraction subclass and implication.  Compare
      ~ ssopab2b .  (Contributed by FL, 6-Nov-2013.)  (Proof shortened by Mario
-     Carneiro, 11-Dec-2016.) $)
+     Carneiro, 11-Dec-2016.)  (New usage is discouraged.) $)
   ssoprab2b $p |- ( { <. <. x , y >. , z >. | ph } C_
     { <. <. x , y >. , z >. | ps } <-> A. x A. y A. z ( ph -> ps ) ) $=
     ( coprab wss wi wal nfoprab1 nfss nfoprab2 nfoprab3 cv wcel oprabid 3imtr3g
@@ -68500,7 +68616,8 @@ ordered pairs (for use in defining operations).  This is a special case
   $}
 
   $( Equivalence of ordered pair abstraction subclass and biconditional.
-     Compare ~ eqopab2b .  (Contributed by Mario Carneiro, 4-Jan-2017.) $)
+     Compare ~ eqopab2b .  (Contributed by Mario Carneiro, 4-Jan-2017.)
+     (New usage is discouraged.) $)
   eqoprab2b $p |- ( { <. <. x , y >. , z >. | ph } =
     { <. <. x , y >. , z >. | ps } <-> A. x A. y A. z ( ph <-> ps ) ) $=
     ( coprab wss wa wi wceq wb ssoprab2b anbi12i eqss 2albiim albii 19.26 bitri
@@ -70528,7 +70645,8 @@ result of an operator (deduction version).  (Contributed by Paul
     $( Implications for the value of an operation, defined by the maps-to
        notation with a class abstraction as a result, having an element.  Here,
        the base set of the class abstraction depends on the first operand.
-       (Contributed by Alexander van der Vekens, 15-Jul-2018.) $)
+       (Contributed by Alexander van der Vekens, 15-Jul-2018.)
+       (New usage is discouraged.) $)
     elovmporab1 $p |- ( Z e. ( X O Y )
                          -> ( X e. _V /\ Y e. _V /\ Z e. [_ X / m ]_ M ) ) $=
       ( cvv wcel wa csb cv wceq nfcv nfel1 co w3a crab elmpocl wsbc cmpo csbeq1
@@ -84919,7 +85037,8 @@ the first case of his notation (simple exponentiation) and subscript it
     nfixp.1 $e |- F/_ y A $.
     nfixp.2 $e |- F/_ y B $.
     $( Bound-variable hypothesis builder for indexed Cartesian product.
-       (Contributed by Mario Carneiro, 15-Oct-2016.) $)
+       (Contributed by Mario Carneiro, 15-Oct-2016.)
+       (New usage is discouraged.) $)
     nfixp $p |- F/_ y X_ x e. A B $=
       ( vz cixp cv wcel cab wfn cfv wa wnfc wtru wal a1i nfeld mptru wral nftru
       df-ixp nfcv weq wn nfcvf adantl nfabd2 nffn df-ral wnf nffvd nfimd nfald2
@@ -108714,13 +108833,13 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
 $)
 
   $( A lemma for proving conditionless ZFC axioms.  (Contributed by NM,
-     1-Jan-2002.) $)
+     1-Jan-2002.)  (New usage is discouraged.) $)
   nd1 $p |- ( A. x x = y -> -. A. x y e. z ) $=
     ( weq wal wel elirrv wsb stdpc4 nfnth elequ1 sbie sylib mto axc11 mtoi ) AB
     DAEBCFZAEQBEZRCCFZCGZRQBCHSQBCIQSBCSBTJBCCKLMNQABOP $.
 
   $( A lemma for proving conditionless ZFC axioms.  (Contributed by NM,
-     1-Jan-2002.) $)
+     1-Jan-2002.)  (New usage is discouraged.) $)
   nd2 $p |- ( A. x x = y -> -. A. x z e. y ) $=
     ( weq wal wel elirrv wsb stdpc4 nfnth elequ2 sbie sylib mto axc11 mtoi ) AB
     DAECBFZAEQBEZRCCFZCGZRQBCHSQBCIQSBCSBTJBCCKLMNQABOP $.
@@ -108732,14 +108851,15 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
     ABAIJKOCLM $.
 
   $( A lemma for proving conditionless ZFC axioms.  (Contributed by NM,
-     2-Jan-2002.) $)
+     2-Jan-2002.)  (New usage is discouraged.) $)
   nd4 $p |- ( A. x x = y -> -. A. z y e. x ) $=
     ( wel wal wn nd3 aecoms ) BADCEFBABACGH $.
 
   ${
     $d x w $.  $d y w $.  $d z w $.
     $( A version of the Axiom of Extensionality with no distinct variable
-       conditions.  (Contributed by NM, 14-Aug-2003.) $)
+       conditions.  (Contributed by NM, 14-Aug-2003.)
+       (New usage is discouraged.) $)
     axextnd $p |- E. x ( ( x e. y <-> x e. z ) -> y = z ) $=
       ( vw wel wb weq wal wex wi wn nfnae wnfc nfcvf nfcrd elequ1 syl6 ax6e ax7
       cv wa nfan adantr adantl nfbid bibi12d a1i cbvald axextg syl6bir 19.8a ex
@@ -108753,7 +108873,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x z w $.  $d x y w $.  $d w ph $.
     $( Lemma for the Axiom of Replacement with no distinct variable conditions.
-       (Contributed by NM, 2-Jan-2002.) $)
+       (Contributed by NM, 2-Jan-2002.)  (New usage is discouraged.) $)
     axrepndlem1 $p |- ( -. A. y y = z -> E. x ( E. y A. z ( ph -> z = y ) ->
                  A. z ( z e. x <-> E. x ( x e. y /\ A. y ph ) ) ) ) $=
       ( vw weq wal wn wi wex wel wa wb nfnae a1i cv imbi12d cbvald exbid adantl
@@ -108771,7 +108891,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
     $d x w $.  $d y w $.  $d z w $.  $d w ph $.
     $( Lemma for the Axiom of Replacement with no distinct variable conditions.
        (Contributed by NM, 2-Jan-2002.)  (Proof shortened by Mario Carneiro,
-       6-Dec-2016.) $)
+       6-Dec-2016.)  (New usage is discouraged.) $)
     axrepndlem2 $p |- ( ( ( -. A. x x = y /\ -. A. x x = z ) /\ -. A. y y = z )
                  -> E. x ( E. y A. z ( ph -> z = y ) ->
                      A. z ( z e. x <-> E. x ( x e. y /\ A. y ph ) ) ) ) $=
@@ -108791,7 +108911,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   $}
 
   $( A version of the Axiom of Replacement with no distinct variable
-     conditions.  (Contributed by NM, 2-Jan-2002.) $)
+     conditions.  (Contributed by NM, 2-Jan-2002.)
+     (New usage is discouraged.) $)
   axrepnd $p |- E. x ( E. y A. z ( ph -> z = y ) ->
                A. z ( A. y z e. x <-> E. x ( A. z x e. y /\ A. y ph ) ) ) $=
     ( weq wal wi wex wa wn nfnae nfan cv wnfc nfcvf2 nfae intnanrd nexd 2falsed
@@ -108809,7 +108930,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x y w $.  $d x z w $.
     $( Lemma for the Axiom of Union with no distinct variable conditions.
-       (Contributed by NM, 2-Jan-2002.) $)
+       (Contributed by NM, 2-Jan-2002.)  (New usage is discouraged.) $)
     axunndlem1 $p |- E. x A. y ( E. x ( y e. x /\ x e. z ) -> y e. x ) $=
       ( vw weq wal wel wa wi wn cv en2lp elequ2 anbi2d mtbii nexdv nfnae exbidv
       wex sps pm2.21d axc4i 19.8ad zfun nfcvf nfcrd nfand nfexd nfimd wb elequ1
@@ -108823,7 +108944,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x w $.  $d y w $.  $d z w $.
     $( A version of the Axiom of Union with no distinct variable conditions.
-       (Contributed by NM, 2-Jan-2002.) $)
+       (Contributed by NM, 2-Jan-2002.)  (New usage is discouraged.) $)
     axunnd $p |- E. x A. y ( E. x ( y e. x /\ x e. z ) -> y e. x ) $=
       ( vw weq wal wel wa wex wi wn nfnae nfan cv wnfc nfcvf adantr nfcvd nfae
       wb axunndlem1 nfv nfeld adantl nfand nfexd nfimd nfald nfcvf2 nfeqd nfan1
@@ -108849,7 +108970,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
     $( Lemma for the Axiom of Power Sets with no distinct variable conditions.
        Revised to remove a redundant antecedent from the consequence.
        (Contributed by NM, 4-Jan-2002.)  (Proof shortened by Mario Carneiro,
-       6-Dec-2016.)  (Revised and shortened by Wolf Lammen, 9-Jun-2019.) $)
+       6-Dec-2016.)  (Revised and shortened by Wolf Lammen, 9-Jun-2019.)
+       (New usage is discouraged.) $)
     axpowndlem2 $p |- ( -. A. x x = y -> ( -. A. x x = z ->
          E. x A. y ( A. x ( E. z x e. y -> A. y x e. z ) -> y e. x ) ) ) $=
       ( vw weq wal wel wex wi wa nfnae cv nfeld adantr nfald adantl wb nfan1 ex
@@ -108870,7 +108992,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
     $d x w $.  $d y z w $.
     $( Lemma for the Axiom of Power Sets with no distinct variable conditions.
        (Contributed by NM, 4-Jan-2002.)  (Revised by Mario Carneiro,
-       10-Dec-2016.)  (Proof shortened by Wolf Lammen, 10-Jun-2019.) $)
+       10-Dec-2016.)  (Proof shortened by Wolf Lammen, 10-Jun-2019.)
+       (New usage is discouraged.) $)
     axpowndlem3 $p |- ( -. x = y ->
                E. x A. y ( A. x ( E. z x e. y -> A. y x e. z ) -> y e. x ) ) $=
       ( vw weq wn wal wel wex wi cv c0 wceq wcel nfnae nfeld adantl exbid nfae
@@ -108892,7 +109015,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
     $d x w $.  $d y w $.  $d z w $.
     $( Lemma for the Axiom of Power Sets with no distinct variable conditions.
        (Contributed by NM, 4-Jan-2002.)  (Proof shortened by Mario Carneiro,
-       10-Dec-2016.) $)
+       10-Dec-2016.)  (New usage is discouraged.) $)
     axpowndlem4 $p |- ( -. A. y y = x -> ( -. A. y y = z -> ( -. x = y
       -> E. x A. y ( A. x ( E. z x e. y -> A. y x e. z ) -> y e. x ) ) ) ) $=
       ( vw weq wal wn wel wi nfnae nfan cv wnfc adantr nfcvd nfeqd nfeld adantl
@@ -108912,7 +109035,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x w $.  $d y w $.
     $( A version of the Axiom of Power Sets with no distinct variable
-       conditions.  (Contributed by NM, 4-Jan-2002.) $)
+       conditions.  (Contributed by NM, 4-Jan-2002.)
+       (New usage is discouraged.) $)
     axpownd $p |- ( -. x = y ->
                E. x A. y ( A. x ( E. z x e. y -> A. y x e. z ) -> y e. x ) ) $=
       ( vw weq wal wn wel wex wi axpowndlem4 axpowndlem1 aecoms a1d wa nfnae cv
@@ -108951,7 +109075,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
 $)
 
   $( Lemma for the Axiom of Regularity with no distinct variable conditions.
-     (Contributed by NM, 3-Jan-2002.) $)
+     (Contributed by NM, 3-Jan-2002.)  (New usage is discouraged.) $)
   axregndlem1 $p |- ( A. x x = z -> ( x e. y ->
                E. x ( x e. y /\ A. z ( z e. x -> -. z e. y ) ) ) ) $=
     ( wel wex weq wal wn wi wa 19.8a nfae elirrv elequ1 mtbii sps alrimi anim2i
@@ -108962,7 +109086,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
     $d x w $.  $d z y w $.
     $( Lemma for the Axiom of Regularity with no distinct variable conditions.
        (Contributed by NM, 3-Jan-2002.)  (Proof shortened by Mario Carneiro,
-       10-Dec-2016.) $)
+       10-Dec-2016.)  (New usage is discouraged.) $)
     axregndlem2 $p |- ( x e. y ->
                  E. x ( x e. y /\ A. z ( z e. x -> -. z e. y ) ) ) $=
       ( vw weq wal wel wn wi wa wex nfnae nfan cv nfcvd wnfc nfcvf nfeld wb ex
@@ -108982,7 +109106,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
     $d x w $.  $d y w $.  $d z w $.
     $( A version of the Axiom of Regularity with no distinct variable
        conditions.  (Contributed by NM, 3-Jan-2002.)  (Proof shortened by Wolf
-       Lammen, 18-Aug-2019.) $)
+       Lammen, 18-Aug-2019.)  (New usage is discouraged.) $)
     axregnd $p |- ( x e. y ->
                  E. x ( x e. y /\ A. z ( z e. x -> -. z e. y ) ) ) $=
       ( vw weq wal wel wn wi wa wex axregndlem2 nfnae wnf cv nfcvf nfcrd adantr
@@ -109036,7 +109160,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   $}
 
   $( Lemma for the Axiom of Choice with no distinct variable conditions.
-     (Contributed by NM, 3-Jan-2002.) $)
+     (Contributed by NM, 3-Jan-2002.)  (New usage is discouraged.) $)
   axacndlem1 $p |- ( A. x x = y ->
             E. x A. y A. z ( A. x ( y e. z /\ z e. w ) -> E. w A. y ( E. w
           ( ( y e. z /\ z e. w ) /\ ( y e. w /\ w e. x ) ) <-> y = w ) ) ) $=
@@ -109045,7 +109169,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
     EUCUAAUAUBMNTUHUEABCOPQRRS $.
 
   $( Lemma for the Axiom of Choice with no distinct variable conditions.
-     (Contributed by NM, 3-Jan-2002.) $)
+     (Contributed by NM, 3-Jan-2002.)  (New usage is discouraged.) $)
   axacndlem2 $p |- ( A. x x = z ->
             E. x A. y A. z ( A. x ( y e. z /\ z e. w ) -> E. w A. y ( E. w
           ( ( y e. z /\ z e. w ) /\ ( y e. w /\ w e. x ) ) <-> y = w ) ) ) $=
@@ -109054,7 +109178,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
     EUCUBAUAUBMNTUHUEACDOPQRRS $.
 
   $( Lemma for the Axiom of Choice with no distinct variable conditions.
-     (Contributed by NM, 3-Jan-2002.) $)
+     (Contributed by NM, 3-Jan-2002.)  (New usage is discouraged.) $)
   axacndlem3 $p |- ( A. y y = z ->
             E. x A. y A. z ( A. x ( y e. z /\ z e. w ) -> E. w A. y ( E. w
           ( ( y e. z /\ z e. w ) /\ ( y e. w /\ w e. x ) ) <-> y = w ) ) ) $=
@@ -109145,13 +109269,13 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
     $d x y z w v u t $.
     $( Axiom of Extensionality ~ ax-ext , reproved from conditionless ZFC
        version and predicate calculus.  (Contributed by NM, 15-Aug-2003.)
-       (Proof modification is discouraged.) $)
+       (Proof modification is discouraged.)  (New usage is discouraged.) $)
     zfcndext $p |- ( A. z ( z e. x <-> z e. y ) -> x = y ) $=
       ( cv wcel wb wceq axextnd 19.36iv ) CDZADZEJBDZEFKLGCCABHI $.
 
     $( Axiom of Replacement ~ ax-rep , reproved from conditionless ZFC axioms.
-       (Contributed by NM, 15-Aug-2003.)
-       (Proof modification is discouraged.) $)
+       (Contributed by NM, 15-Aug-2003.)  (Proof modification is discouraged.)
+       (New usage is discouraged.) $)
     zfcndrep $p |- ( A. w E. y A. z ( A. y ph -> z = y ) ->
                      E. y A. z ( z e. y <-> E. w ( w e. x /\ A. y ph ) ) ) $=
       ( wal cv wceq wi wex wcel wa wb nfe1 nfv nfa1 nfex nfbi nfal exbii elequ2
@@ -109165,8 +109289,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
       ADWTVJVRVOVTECDUAVOVTMWTVNVSEVMVDVLVDCACPURUSTUTVAUGVBVC $.
 
     $( Axiom of Union ~ ax-un , reproved from conditionless ZFC axioms.
-       (Contributed by NM, 15-Aug-2003.)
-       (Proof modification is discouraged.) $)
+       (Contributed by NM, 15-Aug-2003.)  (Proof modification is discouraged.)
+       (New usage is discouraged.) $)
     zfcndun $p |- E. y A. z ( E. w ( z e. w /\ w e. x ) -> z e. y ) $=
       ( cv wcel wa wex wi wal axunnd elequ2 elequ1 anbi12d cbvexvw imbi1i albii
       wceq exbii mpbir ) CEZDEZFZUBAEZFZGZDHZUABEZFZIZCJZBHUIUHUDFZGZBHZUIIZCJZ
@@ -109174,7 +109298,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
 
     $( Axiom of Power Sets ~ ax-pow , reproved from conditionless ZFC axioms.
        The proof uses the "Axiom of Twoness" ~ dtru .  (Contributed by NM,
-       15-Aug-2003.)  (Proof modification is discouraged.) $)
+       15-Aug-2003.)  (Proof modification is discouraged.)
+       (New usage is discouraged.) $)
     zfcndpow $p |- E. y A. z ( A. w ( w e. z -> w e. x ) -> z e. y ) $=
       ( cv wcel wi wal wceq wn dtru exnal mpbir nfe1 axpownd albii imbi1i exbii
       wex elequ1 exlimi ax-mp 19.9v 19.3v imbi12i mpbi imbi12d cbvalvw ) DEZCEZ
@@ -109184,8 +109309,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
       UHQPRM $.
 
     $( Axiom of Regularity ~ ax-reg , reproved from conditionless ZFC axioms.
-       (Contributed by NM, 15-Aug-2003.)
-       (Proof modification is discouraged.) $)
+       (Contributed by NM, 15-Aug-2003.)  (Proof modification is discouraged.)
+       (New usage is discouraged.) $)
     zfcndreg $p |- ( E. y y e. x ->
                  E. y ( y e. x /\ A. z ( z e. y -> -. z e. x ) ) ) $=
       ( cv wcel wn wi wal wa wex nfe1 axregnd exlimi ) BDZADZEZPCDZNEQOEFGCHIZB
@@ -166091,7 +166216,7 @@ seq m ( + , ( n e. ZZ |-> if ( n e. A , [_ n / k ]_ B , 0 ) ) ) ~~> x ) \/
     $( Bound-variable hypothesis builder for sum: if ` x ` is (effectively) not
        free in ` A ` and ` B ` , it is not free in ` sum_ k e. A B ` .
        (Contributed by NM, 11-Dec-2005.)  (Revised by Mario Carneiro,
-       13-Jun-2019.) $)
+       13-Jun-2019.)  (New usage is discouraged.) $)
     nfsum $p |- F/_ x sum_ k e. A B $=
       ( vm vn vz vf cv cfv caddc cz csb cc0 cli c1 cn nfcv csu cuz wss wcel cif
       cmpt cseq wbr wa wrex cfz co wf1o wceq wex wo cio df-sum nfss nfcri nfcsb
@@ -755875,7 +756000,8 @@ coordinates of the intersection points of a (nondegenerate) line and a
     nfiundg.3 $e |- ( ph -> F/_ y B ) $.
     $( Bound-variable hypothesis builder for indexed union.  See ~ nfiund for a
        version with more disjoint variable conditions, but not requiring
-       ~ ax-13 .  (Contributed by Emmett Weisz, 6-Dec-2019.) $)
+       ~ ax-13 .  (Contributed by Emmett Weisz, 6-Dec-2019.)
+       (New usage is discouraged.) $)
     nfiundg $p |- ( ph -> F/_ y U_ x e. A B ) $=
       ( vz ciun cv wcel wrex cab df-iun nfv nfcrd nfrexdg nfabd nfcxfrd ) ACBDE
       JIKELZBDMZINBIDEOAUBCIAIPAUACBDFGACIEHQRST $.

From 8441985d76d8b7107eeb23f8d42ac5bc7235b2d6 Mon Sep 17 00:00:00 2001
From: GinoGiotto <73717712+GinoGiotto@users.noreply.github.com>
Date: Thu, 28 Mar 2024 02:17:15 +0100
Subject: [PATCH 2/4] update discouraged file

---
 discouraged | 1131 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 1131 insertions(+)

diff --git a/discouraged b/discouraged
index ff3040c8a8..f395138174 100755
--- a/discouraged
+++ b/discouraged
@@ -191,11 +191,34 @@
 "1sr" is used by "supsr".
 "1t1e1ALT" is used by "nnmul1com".
 "1t1e1ALT" is used by "remulinvcom".
+"2ax6e" is used by "2sb5rf".
+"2ax6e" is used by "2sb6rf".
+"2ax6e" is used by "2sb6rfOLD".
+"2ax6elem" is used by "2ax6e".
+"2ax6elem" is used by "2ax6eOLD".
+"2eu1" is used by "2eu2".
+"2eu1" is used by "2eu3".
+"2eu1" is used by "2eu3OLD".
+"2eu1" is used by "2eu5OLD".
+"2eu2" is used by "2eu8".
+"2eu7" is used by "2eu8".
+"2euex" is used by "2exeu".
+"2euswap" is used by "2eu1".
+"2euswap" is used by "2eu1OLD".
+"2euswap" is used by "euxfr2".
+"2exeu" is used by "2eu1".
+"2exeu" is used by "2eu1OLD".
+"2exeu" is used by "2eu2".
+"2exeu" is used by "2eu3".
+"2exeu" is used by "2eu3OLD".
 "2llnjN" is used by "2llnm2N".
 "2llnjaN" is used by "2llnjN".
 "2llnm2N" is used by "2llnm3N".
 "2llnma2rN" is used by "cdleme20y".
 "2llnne2N" is used by "2llnneN".
+"2moex" is used by "2eu2".
+"2moex" is used by "2eu5OLD".
+"2moswap" is used by "2euswap".
 "2pm13.193" is used by "2sb5nd".
 "2pm13.193" is used by "2sb5ndALT".
 "2pm13.193" is used by "2sb5ndVD".
@@ -224,6 +247,7 @@
 "2polvalN" is used by "sspmaplubN".
 "2sb5nd" is used by "2uasbanh".
 "2sb5nd" is used by "2uasbanhVD".
+"2sb5rf" is used by "sbel2x".
 "2uasbanh" is used by "2uasban".
 "3atnelvolN" is used by "2atnelvolN".
 "3atnelvolN" is used by "islvol2aN".
@@ -795,10 +819,26 @@
 "adjval" is used by "adjbdln".
 "adjval" is used by "adjval2".
 "adjvalval" is used by "nmopadjlei".
+"aecom" is used by "aecoms".
+"aecom" is used by "naecoms".
+"aecom" is used by "wl-nfae1".
 "aecom-o" is used by "aecoms-o".
 "aecom-o" is used by "aev-o".
 "aecom-o" is used by "ax12indalem".
 "aecom-o" is used by "naecoms-o".
+"aecoms" is used by "axacnd".
+"aecoms" is used by "axacndlem5".
+"aecoms" is used by "axc11".
+"aecoms" is used by "axinfnd".
+"aecoms" is used by "axpownd".
+"aecoms" is used by "axregnd".
+"aecoms" is used by "axrepnd".
+"aecoms" is used by "e2ebind".
+"aecoms" is used by "nd4".
+"aecoms" is used by "wl-ax11-lem1".
+"aecoms" is used by "wl-ax11-lem10".
+"aecoms" is used by "wl-ax11-lem3".
+"aecoms" is used by "wl-ax11-lem9".
 "aecoms-o" is used by "aev-o".
 "aecoms-o" is used by "ax12inda2ALT".
 "aecoms-o" is used by "ax12indalem".
@@ -1401,10 +1441,18 @@
 "ax10fromc7" is used by "axc5c711".
 "ax10fromc7" is used by "equidq".
 "ax10fromc7" is used by "hba1-o".
+"ax12" is used by "axc11-o".
+"ax12" is used by "bj-ax12v3".
+"ax12" is used by "equs5a".
+"ax12" is used by "equs5e".
 "ax12inda2" is used by "ax12inda".
 "ax12indalem" is used by "ax12inda2".
 "ax12indn" is used by "ax12indi".
 "ax12v2-o" is used by "ax12a2-o".
+"ax13" is used by "equvini".
+"ax13" is used by "equviniOLD".
+"ax13" is used by "sbequiALT".
+"ax13" is used by "sbequiOLD".
 "ax13lem1" is used by "ax13".
 "ax13lem1" is used by "ax13lem2".
 "ax13lem1" is used by "ax6e".
@@ -1414,8 +1462,38 @@
 "ax13lem2" is used by "nfeqf2".
 "ax13lem2" is used by "wl-19.2reqv".
 "ax13lem2" is used by "wl-speqv".
+"ax13v" is used by "ax13lem1".
+"ax13v" is used by "wl-spae".
 "ax5el" is used by "dveel2ALT".
 "ax5eq" is used by "dveeq1-o16".
+"ax6" is used by "axc10".
+"ax6e" is used by "2ax6elem".
+"ax6e" is used by "ax6".
+"ax6e" is used by "ax6e2nd".
+"ax6e" is used by "ax6e2ndALT".
+"ax6e" is used by "ax6e2ndVD".
+"ax6e" is used by "ax6er".
+"ax6e" is used by "ax8dfeq".
+"ax6e" is used by "axextnd".
+"ax6e" is used by "axi9".
+"ax6e" is used by "bj-alequex".
+"ax6e" is used by "bj-axc10".
+"ax6e" is used by "dtrucor2".
+"ax6e" is used by "equs4".
+"ax6e" is used by "equsal".
+"ax6e" is used by "equsexALT".
+"ax6e" is used by "equvel".
+"ax6e" is used by "equvini".
+"ax6e" is used by "equviniOLD".
+"ax6e" is used by "exlimiieq1".
+"ax6e" is used by "spd".
+"ax6e" is used by "spei".
+"ax6e" is used by "spim".
+"ax6e" is used by "spimed".
+"ax6e" is used by "spimt".
+"ax6e" is used by "spimvALT".
+"ax6e" is used by "wl-equsald".
+"ax6e" is used by "wl-exeq".
 "ax6e2eq" is used by "ax6e2ndeq".
 "ax6e2eq" is used by "ax6e2ndeqALT".
 "ax6e2eq" is used by "ax6e2ndeqVD".
@@ -1436,11 +1514,45 @@
 "ax9v" is used by "ax9v2".
 "axacnd" is used by "axacprim".
 "axacnd" is used by "zfcndac".
+"axacndlem1" is used by "axacndlem4".
+"axacndlem1" is used by "axacndlem5".
+"axacndlem2" is used by "axacnd".
+"axacndlem2" is used by "axacndlem4".
+"axacndlem3" is used by "axacnd".
+"axacndlem3" is used by "axacndlem5".
 "axacndlem4" is used by "axacndlem5".
 "axacndlem5" is used by "axacnd".
 "axaddf" is used by "axaddcl".
+"axc10" is used by "spALT".
+"axc11" is used by "2sb5ndALT".
+"axc11" is used by "2sb5ndVD".
+"axc11" is used by "ax6e2eq".
+"axc11" is used by "ax6e2eqVD".
+"axc11" is used by "axc11n11".
+"axc11" is used by "bj-hbaeb2".
+"axc11" is used by "dral1".
+"axc11" is used by "dral1ALT".
+"axc11" is used by "hbae".
+"axc11" is used by "nd1".
+"axc11" is used by "nd2".
+"axc11" is used by "wl-aetr".
+"axc11n" is used by "2sb5ndALT".
+"axc11n" is used by "2sb5ndVD".
+"axc11n" is used by "aecom".
+"axc11n" is used by "axi10".
+"axc11n" is used by "e2ebindALT".
+"axc11n" is used by "e2ebindVD".
+"axc11n" is used by "wl-ax11-lem3".
+"axc11n" is used by "wl-ax11-lem8".
+"axc11n" is used by "wl-hbae1".
+"axc15" is used by "ax12".
+"axc15" is used by "ax12b".
+"axc15" is used by "ax12vALT".
+"axc15" is used by "bj-ax12v3ALT".
+"axc15" is used by "equs5".
 "axc16ALT" is used by "axc16gALT".
 "axc16g-o" is used by "ax12inda2".
+"axc16i" is used by "axc16ALT".
 "axc4i-o" is used by "aev-o".
 "axc4i-o" is used by "ax12inda2ALT".
 "axc4i-o" is used by "ax12indalem".
@@ -1456,6 +1568,23 @@
 "axc711" is used by "axc711to11".
 "axc711" is used by "axc711toc7".
 "axc711toc7" is used by "axc711to11".
+"axc9" is used by "ax12eq".
+"axc9" is used by "ax12indalem".
+"axc9" is used by "ax13ALT".
+"axc9" is used by "axbndOLD".
+"axc9" is used by "axc11n11r".
+"axc9" is used by "axextbdist".
+"axc9" is used by "axi12".
+"axc9" is used by "axi12OLD".
+"axc9" is used by "bj-ax6elem1".
+"axc9" is used by "bj-hbaeb2".
+"axc9" is used by "hbae".
+"axc9" is used by "wl-aleq".
+"axextnd" is used by "axextdfeq".
+"axextnd" is used by "axextndbi".
+"axextnd" is used by "axextprim".
+"axextnd" is used by "zfcndext".
+"axi12" is used by "axbnd".
 "axinfnd" is used by "axinfprim".
 "axinfnd" is used by "zfcndinf".
 "axinfndlem1" is used by "axinfnd".
@@ -1476,9 +1605,26 @@
 "axpjpj" is used by "pjpjhth".
 "axpjpj" is used by "pjpo".
 "axpjpj" is used by "pjtoi".
+"axpownd" is used by "axpowprim".
+"axpownd" is used by "zfcndpow".
+"axpowndlem2" is used by "axpowndlem3".
+"axpowndlem3" is used by "axpowndlem4".
+"axpowndlem4" is used by "axpownd".
+"axregnd" is used by "axregprim".
+"axregnd" is used by "zfcndreg".
+"axregndlem1" is used by "axregnd".
+"axregndlem1" is used by "axregndlem2".
+"axregndlem2" is used by "axregnd".
+"axrepnd" is used by "axrepprim".
+"axrepnd" is used by "zfcndrep".
+"axrepndlem1" is used by "axrepndlem2".
+"axrepndlem2" is used by "axrepnd".
 "axresscn" is used by "ax1cn".
 "axresscn" is used by "bj-rrhatsscchat".
 "axsepgfromrep" is used by "axsep".
+"axunnd" is used by "axunprim".
+"axunnd" is used by "zfcndun".
+"axunndlem1" is used by "axunnd".
 "bafval" is used by "cnnvba".
 "bafval" is used by "hhba".
 "bafval" is used by "hhshsslem1".
@@ -2998,8 +3144,132 @@
 "cbncms" is used by "minvecolem4a".
 "cbncms" is used by "ubthlem1".
 "cbncms" is used by "ubthlem2".
+"cbv1" is used by "cbv1h".
+"cbv1" is used by "cbv2".
+"cbv1h" is used by "cbv2h".
+"cbv2" is used by "cbval2".
+"cbv2" is used by "cbvald".
+"cbv2" is used by "sb9".
+"cbv2" is used by "wl-cbvalnaed".
+"cbv2" is used by "wl-sb8t".
+"cbv2h" is used by "cbv2OLD".
+"cbv2h" is used by "eujustALT".
+"cbv3" is used by "axc16i".
+"cbv3" is used by "cbv1".
+"cbv3" is used by "cbv3h".
+"cbv3" is used by "cbval".
+"cbvab" is used by "cbvabvOLD".
+"cbvab" is used by "cbvrab".
+"cbvab" is used by "cbvrabcsf".
+"cbvab" is used by "cbvsbc".
+"cbvab" is used by "cdeqab1".
+"cbval" is used by "cbval2".
+"cbval" is used by "cbval2OLD".
+"cbval" is used by "cbvalv".
+"cbval" is used by "cbvex".
+"cbval" is used by "sb8".
+"cbval2" is used by "cbvex2".
+"cbval2vv" is used by "brfi1indALT".
+"cbvald" is used by "axacnd".
+"cbvald" is used by "axacndlem5".
+"cbvald" is used by "axextdist".
+"cbvald" is used by "axextnd".
+"cbvald" is used by "axinfnd".
+"cbvald" is used by "axpowndlem2".
+"cbvald" is used by "axpowndlem3".
+"cbvald" is used by "axpowndlem4".
+"cbvald" is used by "axregnd".
+"cbvald" is used by "axregndlem2".
+"cbvald" is used by "axrepndlem1".
+"cbvald" is used by "axunndlem1".
+"cbvald" is used by "cbvaldva".
+"cbvald" is used by "cbvexd".
+"cbvald" is used by "distel".
+"cbvald" is used by "wl-sb8eut".
+"cbvaldva" is used by "cbval2vv".
+"cbvalv" is used by "cbval2vv".
+"cbvalv" is used by "cbvexvOLD".
+"cbvalv" is used by "cdeqal1".
+"cbveu" is used by "cbvreu".
+"cbveu" is used by "cbvreucsf".
+"cbvex" is used by "cbveuALT".
+"cbvex" is used by "cbvexv".
+"cbvex" is used by "sb8e".
+"cbvex2vv" is used by "bj-cbvex4vv".
+"cbvex2vv" is used by "cbvex4v".
+"cbvexd" is used by "axacndlem4".
+"cbvexd" is used by "axinfndlem1".
+"cbvexd" is used by "axpownd".
+"cbvexd" is used by "axpowndlem2".
+"cbvexd" is used by "axregndlem2".
+"cbvexd" is used by "axrepndlem2".
+"cbvexd" is used by "axunnd".
+"cbvexd" is used by "cbvexdva".
+"cbvexd" is used by "dfid3".
+"cbvexd" is used by "vtoclgftOLD".
+"cbvexd" is used by "wl-eudf".
+"cbvexd" is used by "wl-mo2df".
+"cbvexdva" is used by "cbvex2vv".
 "cbvexsv" is used by "onfrALTlem1".
 "cbvexsv" is used by "onfrALTlem1VD".
+"cbvexv" is used by "cbvex2vv".
+"cbviing" is used by "cbviinvg".
+"cbviota" is used by "cbviotav".
+"cbviota" is used by "cbvriota".
+"cbviung" is used by "cbviunvg".
+"cbvmo" is used by "cbveuALT".
+"cbvmptfg" is used by "cbvmptg".
+"cbvmptg" is used by "cbvmptvg".
+"cbvopab1g" is used by "cbvmptfg".
+"cbvrab" is used by "cbvrabvOLD".
+"cbvrab" is used by "smfliminf".
+"cbvrab" is used by "smflimsup".
+"cbvrabcsf" is used by "cbvrabv2".
+"cbvrabcsf" is used by "smfinf".
+"cbvrabcsf" is used by "smfinflem".
+"cbvrabcsf" is used by "smfsup".
+"cbvral" is used by "cbviing".
+"cbvral" is used by "cbvral2".
+"cbvral" is used by "cbvralsv".
+"cbvral" is used by "cbvralv".
+"cbvral" is used by "disjxun".
+"cbvral" is used by "ralrnmpt".
+"cbvral" is used by "smfinf".
+"cbvral" is used by "smfinflem".
+"cbvral" is used by "smfsup".
+"cbvral2v" is used by "cbvral3v".
+"cbvralcsf" is used by "cbvralv2".
+"cbvralcsf" is used by "cbvrexcsf".
+"cbvralf" is used by "cbvral".
+"cbvralf" is used by "cbvrexf".
+"cbvralv" is used by "bnj1452".
+"cbvralv" is used by "cbvral2v".
+"cbvralv" is used by "cbvral3v".
+"cbvralv" is used by "disjxun".
+"cbvralv" is used by "frgrwopreglem5ALT".
+"cbvralv" is used by "smfsuplem2".
+"cbvralv" is used by "vonicc".
+"cbvralv" is used by "vonioo".
+"cbvreu" is used by "cbvreuv".
+"cbvreu" is used by "cbvrmo".
+"cbvrex" is used by "cbviung".
+"cbvrex" is used by "cbvrex2".
+"cbvrex" is used by "cbvrexsv".
+"cbvrex" is used by "cbvrexv".
+"cbvrex" is used by "cbvrmo".
+"cbvrexcsf" is used by "cbvrexv2".
+"cbvrexf" is used by "cbvrex".
+"cbvrexsv" is used by "cbvexsv".
+"cbvrexv" is used by "cbvrex2v".
+"cbvrexv" is used by "cygablOLD".
+"cbvrexv" is used by "rexlimdvaacbv".
+"cbvrexv" is used by "smfinf".
+"cbvrexv" is used by "smfinflem".
+"cbvrexv" is used by "smfsup".
+"cbvriota" is used by "cbvriotav".
+"cbvrmo" is used by "cbvrmov".
+"cbvsbc" is used by "cbvcsb".
+"cbvsbc" is used by "cbvsbcv".
 "ccat2s1fvwOLD" is used by "ccat2s1fstOLD".
 "ccatlenOLD" is used by "ccat2s1lenOLD".
 "ccatlenOLD" is used by "wlklenvclwlkOLD".
@@ -4021,6 +4291,16 @@
 "chub2i" is used by "pjclem1".
 "chub2i" is used by "qlaxr3i".
 "chub2i" is used by "sumdmdlem2".
+"chvar" is used by "bnj1384".
+"chvar" is used by "bnj1489".
+"chvar" is used by "chvarv".
+"chvar" is used by "vonhoire".
+"chvar" is used by "vonn0icc2".
+"chvar" is used by "vonn0ioo2".
+"chvar" is used by "zfcndrep".
+"chvarv" is used by "bnj1326".
+"chvarv" is used by "vonicc".
+"chvarv" is used by "vonioo".
 "clmgmOLD" is used by "exidcl".
 "cm0" is used by "chirred".
 "cm2j" is used by "cm2ji".
@@ -4191,6 +4471,7 @@
 "con5" is used by "con5i".
 "con5i" is used by "vk15.4j".
 "con5i" is used by "vk15.4jVD".
+"copsexg" is used by "opabid".
 "crhmsubcALTV" is used by "cringcatALTV".
 "cringcALTV" is used by "cringcatALTV".
 "cringcALTV" is used by "fldcALTV".
@@ -4208,6 +4489,9 @@
 "crngcALTV" is used by "rngccatidALTV".
 "crngcALTV" is used by "rngcrescrhmALTV".
 "crngcALTV" is used by "rngcvalALTV".
+"csbco" is used by "sbccom2".
+"csbnestg" is used by "csbco3g".
+"csbnestgf" is used by "csbnestg".
 "csbopabgALT" is used by "csbcnvgALT".
 "cvati" is used by "cvbr4i".
 "cvbr" is used by "cvbr2".
@@ -4745,7 +5029,22 @@
 "dfpjop" is used by "elpjhmop".
 "dfpjop" is used by "elpjidm".
 "dfpjop" is used by "pjhmopidm".
+"dfsb1" is used by "bj-dfsb2".
+"dfsb1" is used by "drsb1".
+"dfsb1" is used by "equsb1vOLDOLD".
+"dfsb1" is used by "frege55b".
+"dfsb1" is used by "sb2vOLDOLD".
+"dfsb1" is used by "sbequ1OLD".
+"dfsb1" is used by "sbequ2OLDOLD".
+"dfsb1" is used by "sbimdOLD".
+"dfsb1" is used by "sbimdvOLD".
+"dfsb1" is used by "sbimiOLD".
+"dfsb1" is used by "sbnOLD".
+"dfsb1" is used by "sbtvOLD".
+"dfsb1" is used by "subsym1".
+"dfsb2" is used by "dfsb3".
 "dfsb2ALT" is used by "dfsb3ALT".
+"dfsb3" is used by "sbnOLD".
 "dfsb3ALT" is used by "sbnALT".
 "dfvd1imp" is used by "gen11".
 "dfvd1impr" is used by "gen11".
@@ -5110,26 +5409,102 @@
 "docavalN" is used by "diaocN".
 "docavalN" is used by "docaclN".
 "dochfN" is used by "dochpolN".
+"dral1" is used by "axc16gALT".
+"dral1" is used by "axpownd".
+"dral1" is used by "drex1".
+"dral1" is used by "drnf1".
+"dral1" is used by "ralcom2".
+"dral1" is used by "sb9".
+"dral1" is used by "wl-ax11-lem5".
+"dral1" is used by "wl-ax11-lem8".
+"dral1" is used by "wl-ax11-lem9".
+"dral1" is used by "wl-dral1d".
 "dral1-o" is used by "ax12fromc15".
 "dral1-o" is used by "ax12inda2ALT".
 "dral1-o" is used by "ax12indalem".
 "dral1-o" is used by "axc16g-o".
+"dral2" is used by "axpownd".
+"dral2" is used by "dral1ALT".
+"dral2" is used by "drnfc1OLD".
+"dral2" is used by "sbal1".
+"dral2" is used by "sbal2".
+"dral2" is used by "sbal2OLD".
+"dral2" is used by "wl-sbalnae".
 "dral2-o" is used by "ax12el".
 "dral2-o" is used by "ax12eq".
 "dral2-o" is used by "ax12inda2ALT".
 "dral2-o" is used by "ax12indalem".
+"drex1" is used by "copsexg".
+"drex1" is used by "dfid3".
+"drex1" is used by "dropab1".
+"drex1" is used by "dropab2".
+"drex1" is used by "drsb1".
+"drex1" is used by "e2ebind".
+"drex1" is used by "e2ebindALT".
+"drex1" is used by "e2ebindVD".
+"drex1" is used by "eujustALT".
+"drex1" is used by "exdistrf".
+"drex2" is used by "dfid3".
+"drex2" is used by "dropab1".
+"drex2" is used by "dropab2".
+"drex2" is used by "e2ebind".
 "drhmsubcALTV" is used by "fldhmsubcALTV".
+"drnf1" is used by "drnfc1".
+"drnf1" is used by "drnfc1OLD".
+"drnf1" is used by "nfald2".
+"drnf1" is used by "wl-nfs1t".
+"drnf2" is used by "drnfc2".
+"drnf2" is used by "nfsb4t".
+"drnf2" is used by "nfsb4tALT".
+"drnfc1" is used by "bj-nfcsym".
+"drnfc1" is used by "nfabd2".
+"drnfc1" is used by "nfabd2OLD".
+"drnfc1" is used by "nfcvb".
+"drnfc1" is used by "nfriotad".
 "drngoi" is used by "dvrunz".
 "drngoi" is used by "fldcrng".
+"drsb1" is used by "ichnfimlem2".
+"drsb1" is used by "iotaeq".
+"drsb1" is used by "sb2ae".
+"drsb1" is used by "sbco3".
 "dvadiaN" is used by "diarnN".
+"dveel1" is used by "distel".
+"dveel2" is used by "axc14".
+"dveeq1" is used by "axc11n".
+"dveeq1" is used by "nfeqf".
 "dveeq1-o" is used by "ax12inda2ALT".
+"dveeq2" is used by "axc15".
+"dveeq2" is used by "axc15OLD".
 "dveeq2-o" is used by "ax12el".
 "dveeq2-o" is used by "ax12eq".
 "dveeq2-o" is used by "ax12inda".
 "dveeq2-o" is used by "ax12v2-o".
+"dvelim" is used by "axc14".
+"dvelim" is used by "dvelimv".
+"dvelim" is used by "eujustALT".
+"dvelimc" is used by "nfcvfOLD".
+"dvelimdc" is used by "dvelimc".
+"dvelimdf" is used by "dvelimdc".
+"dvelimdf" is used by "nfsb4t".
+"dvelimdf" is used by "nfsb4tALT".
+"dvelimf" is used by "dvelimdf".
+"dvelimf" is used by "dvelimh".
+"dvelimf" is used by "dvelimnf".
 "dvelimf-o" is used by "ax12el".
 "dvelimf-o" is used by "dveeq1-o".
 "dvelimf-o" is used by "dveeq2-o".
+"dvelimh" is used by "ax6e2nd".
+"dvelimh" is used by "ax6e2ndALT".
+"dvelimh" is used by "ax6e2ndVD".
+"dvelimh" is used by "dveel2ALT".
+"dvelimh" is used by "dveeq1-o16".
+"dvelimh" is used by "dvelim".
+"dvelimnf" is used by "nfcvf".
+"dvelimnf" is used by "nfrab".
+"dvelimv" is used by "dveel1".
+"dvelimv" is used by "dveel2".
+"dvelimv" is used by "dveeq2ALT".
+"dvelimv" is used by "rgen2a".
 "dvh3dimatN" is used by "dvh2dimatN".
 "dvhopaddN" is used by "dvhopN".
 "dvhopspN" is used by "dvhopN".
@@ -5831,6 +6206,8 @@
 "enrex" is used by "mulclsr".
 "enrex" is used by "mulsrpr".
 "enrex" is used by "recexsrlem".
+"eqopab2b" is used by "opabbi".
+"eqoprab2b" is used by "oprabbi".
 "eqresr" is used by "ax1ne0".
 "eqresr" is used by "axpre-lttri".
 "eqresr" is used by "axrrecex".
@@ -5839,7 +6216,39 @@
 "equid1" is used by "equcomi1".
 "equidqe" is used by "axc5sp1".
 "equidqe" is used by "equidq".
+"equs4" is used by "bj-sbsb".
+"equs4" is used by "equs45f".
+"equs4" is used by "equs5".
+"equs4" is used by "equsex".
+"equs4" is used by "sb1OLD".
+"equs4" is used by "sb2ALT".
+"equs45f" is used by "sb5f".
+"equs45f" is used by "sb5fALT".
+"equs5" is used by "bj-sbsb".
+"equs5" is used by "sb3OLD".
+"equs5" is used by "sb3b".
+"equs5" is used by "sb4ALT".
+"equs5a" is used by "equs45f".
+"equs5a" is used by "sb4aALT".
+"equs5e" is used by "sb4e".
+"equsal" is used by "bj-sbievv".
+"equsal" is used by "dvelimf".
+"equsal" is used by "equsalh".
+"equsal" is used by "equsex".
+"equsal" is used by "sb6rf".
+"equsal" is used by "sb6x".
+"equsalh" is used by "dvelimf-o".
+"equsb1" is used by "frege54cor1b".
+"equsb1" is used by "pm13.183OLD".
+"equsb1" is used by "sb5ALT".
+"equsb1" is used by "sb5ALTVD".
+"equsb1" is used by "sbequ8".
+"equsb1" is used by "sbie".
 "equsb1ALT" is used by "sbieALT".
+"equsb2" is used by "bj-sbidmOLD".
+"equsex" is used by "equsexh".
+"equsex" is used by "sb5rf".
+"equvini" is used by "2ax6elem".
 "erngbase-rN" is used by "erngdvlem1-rN".
 "erngbase-rN" is used by "erngdvlem2-rN".
 "erngbase-rN" is used by "erngdvlem3-rN".
@@ -5865,7 +6274,9 @@
 "erngset-rN" is used by "erngbase-rN".
 "erngset-rN" is used by "erngfmul-rN".
 "erngset-rN" is used by "erngfplus-rN".
+"euxfr2" is used by "euxfr".
 "exatleN" is used by "cdlema2N".
+"exdistrf" is used by "oprabid".
 "exidu1" is used by "cmpidelt".
 "exidu1" is used by "exidresid".
 "exidu1" is used by "iorlid".
@@ -6349,6 +6760,11 @@
 "hba1-o" is used by "axc711toc7".
 "hba1-o" is used by "dvelimf-o".
 "hba1-o" is used by "nfa1-o".
+"hbabg" is used by "bnj1441g".
+"hbabg" is used by "nfsabg".
+"hbae" is used by "ax6e2eq".
+"hbae" is used by "hbnae".
+"hbae" is used by "nfae".
 "hbae-o" is used by "aev-o".
 "hbae-o" is used by "dral1-o".
 "hbae-o" is used by "dral2-o".
@@ -6356,13 +6772,28 @@
 "hbalg" is used by "hbexgVD".
 "hbequid" is used by "equidq".
 "hbequid" is used by "nfequid-o".
+"hbnae" is used by "ax6e2nd".
+"hbnae" is used by "ax6e2ndALT".
+"hbnae" is used by "ax6e2ndVD".
+"hbnae" is used by "ax6e2ndeqALT".
+"hbnae" is used by "ax6e2ndeqVD".
+"hbnae" is used by "bj-hbnaeb".
+"hbnae" is used by "eujustALT".
+"hbnae" is used by "hbnaes".
 "hbnae-o" is used by "ax12inda2ALT".
 "hbnae-o" is used by "ax12indalem".
 "hbnae-o" is used by "dvelimf-o".
 "hbntal" is used by "hbexgVD".
 "hbntal" is used by "hbimpg".
 "hbntal" is used by "hbimpgVD".
+"hbsb" is used by "hbabg".
+"hbsb" is used by "hblemg".
+"hbsb2" is used by "nfsb2".
 "hbsb2ALT" is used by "nfsb2ALT".
+"hbsb2a" is used by "bj-hbsb3t".
+"hbsb2a" is used by "hbsb3".
+"hbsb3" is used by "axc16ALT".
+"hbsb3" is used by "nfs1".
 "hcau" is used by "chscllem2".
 "hcau" is used by "hcaucvg".
 "hcau" is used by "hcauseq".
@@ -9306,6 +9737,8 @@
 "mndomgmid" is used by "isdrngo2".
 "mndomgmid" is used by "ismndo2".
 "mndomgmid" is used by "rngoidmlem".
+"moexex" is used by "2moswap".
+"moexex" is used by "moexexv".
 "mpv" is used by "mulcompr".
 "mulassnq" is used by "1idpr".
 "mulassnq" is used by "addclprlem2".
@@ -9526,14 +9959,287 @@
 "mulsrpr" is used by "mulcomsr".
 "mulsrpr" is used by "mulgt0sr".
 "mulsrpr" is used by "recexsrlem".
+"naecoms" is used by "axpowndlem2".
+"naecoms" is used by "eujustALT".
+"naecoms" is used by "nfcvf2".
+"naecoms" is used by "sb9".
+"naecoms" is used by "wl-eudf".
+"naecoms" is used by "wl-mo2df".
+"naecoms" is used by "wl-sbcom2d".
 "naecoms-o" is used by "ax12inda2ALT".
+"nd1" is used by "axacndlem1".
+"nd1" is used by "axacndlem2".
+"nd1" is used by "axinfnd".
+"nd1" is used by "axinfndlem1".
+"nd1" is used by "axrepnd".
+"nd2" is used by "axacndlem4".
+"nd2" is used by "axinfndlem1".
+"nd2" is used by "axpownd".
+"nd2" is used by "axrepnd".
+"nd4" is used by "axrepnd".
 "nfa1-o" is used by "ax12el".
 "nfa1-o" is used by "ax12eq".
 "nfa1-o" is used by "ax12v2-o".
 "nfa1-o" is used by "axc11n-16".
+"nfabd" is used by "nfabd2".
+"nfabd" is used by "nfcsbd".
+"nfabd" is used by "nfiotad".
+"nfabd" is used by "nfiundg".
+"nfabd" is used by "nfsbcd".
+"nfabd2" is used by "nfabdOLD".
+"nfabd2" is used by "nfixp".
+"nfabd2" is used by "nfrab".
+"nfabg" is used by "nfaba1g".
+"nfabg" is used by "nfiing".
+"nfabg" is used by "nfiung".
+"nfae" is used by "2ax6elem".
+"nfae" is used by "axacnd".
+"nfae" is used by "axacndlem1".
+"nfae" is used by "axacndlem2".
+"nfae" is used by "axacndlem3".
+"nfae" is used by "axacndlem4".
+"nfae" is used by "axacndlem5".
+"nfae" is used by "axbnd".
+"nfae" is used by "axc16nfALT".
+"nfae" is used by "axi12OLD".
+"nfae" is used by "axpownd".
+"nfae" is used by "axpowndlem3".
+"nfae" is used by "axregnd".
+"nfae" is used by "axregndlem1".
+"nfae" is used by "axrepnd".
+"nfae" is used by "axunnd".
+"nfae" is used by "dral2".
+"nfae" is used by "drex2".
+"nfae" is used by "drnf2".
+"nfae" is used by "nfnae".
+"nfae" is used by "sbalOLD".
+"nfae" is used by "sbco3".
+"nfae" is used by "sbequ5".
+"nfald2" is used by "dvelimf".
+"nfald2" is used by "nfexd2".
+"nfald2" is used by "nfiotad".
+"nfald2" is used by "nfixp".
+"nfald2" is used by "nfmod2".
+"nfald2" is used by "nfrald".
+"nfcdeq" is used by "nfccdeq".
+"nfcsb" is used by "cbvrabcsf".
+"nfcsb" is used by "cbvralcsf".
+"nfcsb" is used by "cbvreucsf".
+"nfcsb" is used by "elfvmptrab1".
+"nfcsb" is used by "elovmporab1".
+"nfcsb" is used by "nfsum".
+"nfcsbd" is used by "nfcsb".
+"nfcvf" is used by "axacnd".
+"nfcvf" is used by "axacndlem4".
+"nfcvf" is used by "axacndlem5".
+"nfcvf" is used by "axextdist".
+"nfcvf" is used by "axextnd".
+"nfcvf" is used by "axinfnd".
+"nfcvf" is used by "axinfndlem1".
+"nfcvf" is used by "axpowndlem2".
+"nfcvf" is used by "axpowndlem4".
+"nfcvf" is used by "axregnd".
+"nfcvf" is used by "axregndlem2".
+"nfcvf" is used by "axrepnd".
+"nfcvf" is used by "axrepndlem2".
+"nfcvf" is used by "axunnd".
+"nfcvf" is used by "axunndlem1".
+"nfcvf" is used by "bj-nfcsym".
+"nfcvf" is used by "nfcvb".
+"nfcvf" is used by "nfcvf2".
+"nfcvf" is used by "nfdisj".
+"nfcvf" is used by "nfixp".
+"nfcvf" is used by "nfrald".
+"nfcvf" is used by "nfreud".
+"nfcvf" is used by "nfriotad".
+"nfcvf" is used by "nfrmo".
+"nfcvf" is used by "nfrmod".
+"nfcvf" is used by "ralcom2".
+"nfcvf2" is used by "axacnd".
+"nfcvf2" is used by "axacndlem4".
+"nfcvf2" is used by "axacndlem5".
+"nfcvf2" is used by "axinfnd".
+"nfcvf2" is used by "axinfndlem1".
+"nfcvf2" is used by "axpownd".
+"nfcvf2" is used by "axpowndlem3".
+"nfcvf2" is used by "axpowndlem4".
+"nfcvf2" is used by "axregndlem2".
+"nfcvf2" is used by "axrepnd".
+"nfcvf2" is used by "axrepndlem1".
+"nfcvf2" is used by "axrepndlem2".
+"nfcvf2" is used by "axunnd".
+"nfcvf2" is used by "bj-nfcsym".
+"nfcvf2" is used by "dfid3".
+"nfcvf2" is used by "oprabid".
+"nfeqf" is used by "2ax6elem".
+"nfeqf" is used by "axc9".
+"nfeqf" is used by "dvelimf".
+"nfeqf" is used by "equvel".
+"nfeqf" is used by "wl-2sb6d".
+"nfeqf" is used by "wl-equsb4".
+"nfeqf" is used by "wl-exeq".
+"nfeqf" is used by "wl-nfeqfb".
+"nfeqf" is used by "wl-sbalnae".
+"nfeqf1" is used by "dveeq1".
+"nfeqf1" is used by "nfiotad".
+"nfeqf1" is used by "nfmod2".
+"nfeqf1" is used by "sbal2".
+"nfeqf1" is used by "sbal2OLD".
+"nfeqf1" is used by "wl-eudf".
+"nfeqf1" is used by "wl-mo2df".
+"nfeqf2" is used by "axpowndlem2".
+"nfeqf2" is used by "axpowndlem3".
+"nfeqf2" is used by "axrepndlem1".
+"nfeqf2" is used by "bj-dvelimdv".
+"nfeqf2" is used by "bj-dvelimdv1".
+"nfeqf2" is used by "copsexg".
+"nfeqf2" is used by "dveeq2".
+"nfeqf2" is used by "nfeqf1".
+"nfeqf2" is used by "sb4b".
+"nfeqf2" is used by "sb4bOLD".
+"nfeqf2" is used by "sbal1".
+"nfeqf2" is used by "wl-equsb3".
+"nfeqf2" is used by "wl-eudf".
+"nfeqf2" is used by "wl-euequf".
+"nfeqf2" is used by "wl-mo2df".
+"nfeqf2" is used by "wl-sbcom2d-lem1".
+"nfeu" is used by "2eu7".
+"nfeu" is used by "2eu8".
+"nfeu" is used by "bnj1489".
+"nfeud" is used by "nfeu".
+"nfeud2" is used by "nfeud".
+"nfeud2" is used by "nfreud".
+"nfexd2" is used by "nfeud2".
+"nfiota" is used by "nfsum".
+"nfiotad" is used by "nfiota".
+"nfiotad" is used by "nfriotad".
+"nfixp" is used by "vonioo".
+"nfmo" is used by "2euex".
+"nfmo" is used by "2moex".
+"nfmo" is used by "moexex".
+"nfmod" is used by "nfmo".
+"nfmod" is used by "wl-mo3t".
+"nfmod2" is used by "nfdisj".
+"nfmod2" is used by "nfeud2".
+"nfmod2" is used by "nfmod".
+"nfmod2" is used by "nfrmo".
+"nfmod2" is used by "nfrmod".
+"nfnae" is used by "2ax6elem".
+"nfnae" is used by "ax6e2ndeq".
+"nfnae" is used by "ax6e2ndeqVD".
+"nfnae" is used by "axacnd".
+"nfnae" is used by "axacndlem4".
+"nfnae" is used by "axacndlem5".
+"nfnae" is used by "axbndOLD".
+"nfnae" is used by "axextbdist".
+"nfnae" is used by "axextdist".
+"nfnae" is used by "axextnd".
+"nfnae" is used by "axinfnd".
+"nfnae" is used by "axinfndlem1".
+"nfnae" is used by "axpownd".
+"nfnae" is used by "axpowndlem2".
+"nfnae" is used by "axpowndlem3".
+"nfnae" is used by "axpowndlem4".
+"nfnae" is used by "axregnd".
+"nfnae" is used by "axregndlem2".
+"nfnae" is used by "axrepnd".
+"nfnae" is used by "axrepndlem1".
+"nfnae" is used by "axrepndlem2".
+"nfnae" is used by "axunnd".
+"nfnae" is used by "axunndlem1".
+"nfnae" is used by "dfid3".
+"nfnae" is used by "distel".
+"nfnae" is used by "dvelimf".
+"nfnae" is used by "nfabd2".
+"nfnae" is used by "nfabd2OLD".
+"nfnae" is used by "nfald2".
+"nfnae" is used by "nfriotad".
+"nfnae" is used by "nfsb4t".
+"nfnae" is used by "nfsb4tALT".
+"nfnae" is used by "ralcom2".
+"nfnae" is used by "sb9".
+"nfnae" is used by "sbal1".
+"nfnae" is used by "sbal2".
+"nfnae" is used by "sbal2OLD".
+"nfnae" is used by "sbco2".
+"nfnae" is used by "sbco2ALT".
+"nfnae" is used by "sbco3".
+"nfnae" is used by "sbequ6".
+"nfnae" is used by "wl-2sb6d".
+"nfnae" is used by "wl-cbvalnaed".
+"nfnae" is used by "wl-eudf".
+"nfnae" is used by "wl-eutf".
+"nfnae" is used by "wl-mo2df".
+"nfnae" is used by "wl-mo2tf".
+"nfnae" is used by "wl-sbalnae".
+"nfra2" is used by "ralcom2".
+"nfrab" is used by "elfvmptrab1".
+"nfrab" is used by "elovmporab1".
+"nfrab" is used by "smfinfmpt".
+"nfrab" is used by "smflimsuplem7".
+"nfrab" is used by "smfsupmpt".
+"nfrab" is used by "smfsupxr".
+"nfral" is used by "bnj1228".
+"nfral" is used by "cbvral2".
+"nfral" is used by "disjxun".
+"nfral" is used by "eliuniincex".
+"nfral" is used by "nfiing".
+"nfral" is used by "nfra2".
+"nfral" is used by "opreu2reuALT".
+"nfral" is used by "smfinf".
+"nfral" is used by "smfsup".
+"nfrald" is used by "nfral".
+"nfrald" is used by "nfrexdg".
+"nfreud" is used by "nfreu".
+"nfrexdg" is used by "nfiundg".
+"nfrexdg" is used by "nfrexg".
+"nfrexg" is used by "nfiung".
+"nfs1" is used by "sb8".
+"nfs1" is used by "sb8e".
+"nfsabg" is used by "nfabg".
+"nfsb" is used by "2sb5nd".
+"nfsb" is used by "2sb8e".
+"nfsb" is used by "ax11-pm2".
+"nfsb" is used by "cbviota".
+"nfsb" is used by "cbvmptfg".
+"nfsb" is used by "cbvopab1g".
+"nfsb" is used by "cbvrab".
+"nfsb" is used by "cbvrabcsf".
+"nfsb" is used by "cbvralf".
+"nfsb" is used by "cbvralsv".
+"nfsb" is used by "cbvreu".
+"nfsb" is used by "cbvreucsf".
+"nfsb" is used by "cbvrexsv".
+"nfsb" is used by "cbvriota".
+"nfsb" is used by "dfich2OLD".
+"nfsb" is used by "dfich2ai".
+"nfsb" is used by "hbsb".
+"nfsb" is used by "sb10f".
+"nfsb" is used by "sb8eu".
+"nfsb" is used by "sb8iota".
+"nfsb2" is used by "nfsb4t".
+"nfsb2" is used by "sb9".
+"nfsb2" is used by "sbco3".
+"nfsb2" is used by "wl-nfs1t".
 "nfsb2ALT" is used by "nfsb4tALT".
+"nfsb4" is used by "nfsbOLD".
+"nfsb4" is used by "sbco2".
 "nfsb4ALT" is used by "sbco2ALT".
+"nfsb4t" is used by "ichnfimlem1".
+"nfsb4t" is used by "nfsb4".
+"nfsb4t" is used by "nfsbd".
 "nfsb4tALT" is used by "nfsb4ALT".
+"nfsbc" is used by "cbvralcsf".
+"nfsbc" is used by "elovmporab1".
+"nfsbc" is used by "opreu2reuALT".
+"nfsbc" is used by "ralrnmpt".
+"nfsbcd" is used by "nfcsbd".
+"nfsbcd" is used by "nfsbc".
+"nfsbcd" is used by "sbcnestgf".
+"nfsbd" is used by "nfabd".
+"nfsbd" is used by "nfabd2OLD".
+"nfsbd" is used by "nfsb".
+"nfsbd" is used by "wl-sb8eut".
 "nic-ax" is used by "lukshef-ax1".
 "nic-ax" is used by "nic-id".
 "nic-ax" is used by "nic-idlem1".
@@ -10688,6 +11394,8 @@
 "onsetreclem1" is used by "onsetreclem3".
 "onsetreclem2" is used by "onsetrec".
 "onsetreclem3" is used by "onsetrec".
+"opabid" is used by "brabidga".
+"opabid" is used by "ssopab2b".
 "opabresidOLD" is used by "mptresidOLD".
 "opelcn" is used by "axicn".
 "opelopabsbALT" is used by "brabsb2".
@@ -10704,6 +11412,7 @@
 "opidon2OLD" is used by "exidreslem".
 "opidonOLD" is used by "opidon2OLD".
 "opidonOLD" is used by "rngopidOLD".
+"oprabid" is used by "ssoprab2b".
 "opsqrlem2" is used by "opsqrlem6".
 "opsqrlem3" is used by "opsqrlem4".
 "opsqrlem3" is used by "opsqrlem5".
@@ -11429,6 +12138,8 @@
 "psubspi2N" is used by "pclfinN".
 "psubspi2N" is used by "pclfinclN".
 "qexALT" is used by "reexALT".
+"ralcom2" is used by "tratrbVD".
+"ralrnmpt" is used by "rexrnmpt".
 "rb-ax1" is used by "rblem1".
 "rb-ax1" is used by "rblem2".
 "rb-ax1" is used by "rblem4".
@@ -11787,10 +12498,26 @@
 "rngoueqz" is used by "isdmn3".
 "rspsbc2" is used by "tratrb".
 "rspsbc2" is used by "tratrbVD".
+"sb1" is used by "dfsb1".
+"sb1" is used by "sb3bOLD".
+"sb1" is used by "sb4e".
+"sb1" is used by "sb4vOLDOLD".
+"sb1" is used by "spsbeOLDOLD".
 "sb1ALT" is used by "sb4ALT".
 "sb1ALT" is used by "sb4aALT".
 "sb1ALT" is used by "sb4vOLDALT".
 "sb1ALT" is used by "spsbeALT".
+"sb2" is used by "dfsb2".
+"sb2" is used by "equsb1".
+"sb2" is used by "equsb2".
+"sb2" is used by "hbsb2".
+"sb2" is used by "hbsb2a".
+"sb2" is used by "hbsb2e".
+"sb2" is used by "sb3OLD".
+"sb2" is used by "sb6f".
+"sb2" is used by "sbeqal1".
+"sb2" is used by "sbequiOLD".
+"sb2" is used by "sbi1OLD".
 "sb2ALT" is used by "dfsb2ALT".
 "sb2ALT" is used by "equsb1ALT".
 "sb2ALT" is used by "hbsb2ALT".
@@ -11802,22 +12529,63 @@
 "sb2vOLD" is used by "sb6OLD".
 "sb2vOLD" is used by "sbi1vOLD".
 "sb2vOLDALT" is used by "sb6ALT".
+"sb3" is used by "dfsb1".
+"sb3" is used by "sb3bOLD".
+"sb3b" is used by "sb1".
+"sb3b" is used by "sb3".
 "sb4ALT" is used by "dfsb2ALT".
 "sb4ALT" is used by "hbsb2ALT".
 "sb4ALT" is used by "sbequiALT".
 "sb4ALT" is used by "sbi1ALT".
 "sb4OLD" is used by "sbequiOLD".
 "sb4OLD" is used by "sbi1OLD".
+"sb4a" is used by "hbsb2a".
+"sb4a" is used by "sb6f".
 "sb4aALT" is used by "sb6fALT".
+"sb4b" is used by "dfsb2".
+"sb4b" is used by "hbsb2".
+"sb4b" is used by "sb1OLD".
+"sb4b" is used by "sb2".
+"sb4b" is used by "sb3b".
+"sb4b" is used by "sb4OLD".
+"sb4b" is used by "sb4a".
+"sb4b" is used by "sbal1".
+"sb4b" is used by "sbal2".
+"sb4b" is used by "sbal2OLD".
+"sb4b" is used by "sbcom3".
+"sb4b" is used by "wl-2sb6d".
+"sb4b" is used by "wl-sbalnae".
+"sb4e" is used by "hbsb2e".
 "sb4vOLD" is used by "sb6OLD".
 "sb4vOLD" is used by "sbi1vOLD".
 "sb4vOLDALT" is used by "sb6ALT".
 "sb5ALT2" is used by "sb7fALT".
+"sb5f" is used by "sb7f".
 "sb5fALT" is used by "sb7fALT".
 "sb6ALT" is used by "sb5ALT2".
+"sb6f" is used by "bj-sbievv".
+"sb6f" is used by "sb5f".
 "sb6fALT" is used by "sb5fALT".
+"sb7f" is used by "dfsb7OLDOLD".
+"sb7f" is used by "sb7h".
 "sb7fALT" is used by "dfsb7ALT".
+"sb8" is used by "ax11-pm2".
+"sb8" is used by "sb8iota".
+"sb8" is used by "sbhb".
+"sb8" is used by "wl-sb8eut".
+"sb8e" is used by "2sb8e".
+"sb8e" is used by "bnj985".
+"sb8e" is used by "exlimddvfi".
+"sb8e" is used by "pm11.58".
+"sb8e" is used by "sb8mo".
+"sb8eu" is used by "cbveu".
+"sb8eu" is used by "cbvreu".
+"sb8eu" is used by "sb8mo".
+"sb8mo" is used by "cbvmo".
+"sb9" is used by "sb9i".
 "sbal1" is used by "sbalOLD".
+"sbal2" is used by "2sb5ndALT".
+"sbal2" is used by "2sb5ndVD".
 "sbanALT" is used by "sbbiALT".
 "sbanvOLD" is used by "sbbivOLD".
 "sbbiALT" is used by "sblbisALT".
@@ -11829,9 +12597,29 @@
 "sbc3or" is used by "sbcoreleleq".
 "sbcbi" is used by "sbcssgVD".
 "sbcbi" is used by "trsbcVD".
+"sbcco" is used by "csbco".
+"sbcco" is used by "sbccom2".
+"sbcco" is used by "sbccom2f".
 "sbcim2g" is used by "trsbc".
 "sbcim2g" is used by "trsbcVD".
+"sbcnestg" is used by "sbcco3g".
+"sbcnestgf" is used by "csbnestgf".
+"sbcnestgf" is used by "sbcnestg".
+"sbco" is used by "sbco3".
+"sbco" is used by "sbid2".
+"sbco2" is used by "cbvab".
+"sbco2" is used by "clelsb3f".
+"sbco2" is used by "clelsb3fOLD".
+"sbco2" is used by "sb7f".
+"sbco2" is used by "sbcco".
+"sbco2" is used by "sbco2d".
 "sbco2ALT" is used by "sb7fALT".
+"sbco2d" is used by "sbco3".
+"sbco2d" is used by "wl-clelsb3df".
+"sbco3" is used by "sbcom".
+"sbcom3" is used by "sbco".
+"sbcom3" is used by "sbcom".
+"sbcom3" is used by "sbidm".
 "sbcoreleleq" is used by "tratrb".
 "sbcoreleleq" is used by "tratrbVD".
 "sbcrexgOLD" is used by "2sbcrexOLD".
@@ -11855,8 +12643,37 @@
 "sbi1ALT" is used by "sbimALT".
 "sbi1vOLD" is used by "sbimvOLD".
 "sbi2ALT" is used by "sbimALT".
+"sbid2" is used by "sbid2v".
+"sbid2" is used by "sbtrt".
+"sbid2v" is used by "dfich2bi".
+"sbie" is used by "2sbiev".
+"sbie" is used by "bj-sbeqALT".
+"sbie" is used by "bnj1321".
+"sbie" is used by "cbvab".
+"sbie" is used by "cbveu".
+"sbie" is used by "cbviota".
+"sbie" is used by "cbvmo".
+"sbie" is used by "cbvmptfg".
+"sbie" is used by "cbvopab1g".
+"sbie" is used by "cbvrab".
+"sbie" is used by "cbvrabcsf".
+"sbie" is used by "cbvralcsf".
+"sbie" is used by "cbvralf".
+"sbie" is used by "cbvreu".
+"sbie" is used by "cbvreucsf".
+"sbie" is used by "cbvriota".
+"sbie" is used by "clelsb3fOLD".
+"sbie" is used by "nd1".
+"sbie" is used by "nd2".
+"sbie" is used by "nfcdeq".
+"sbie" is used by "sbcrexgOLD".
+"sbie" is used by "sbied".
 "sbieALT" is used by "sbiedALT".
+"sbied" is used by "sbco2".
+"sbied" is used by "sbiedv".
+"sbied" is used by "wl-equsb3".
 "sbiedALT" is used by "sbco2ALT".
+"sbiedv" is used by "2sbiev".
 "sbimALT" is used by "sbanALT".
 "sbimALT" is used by "sbbiALT".
 "sbimALT" is used by "sbrimALT".
@@ -11872,6 +12689,7 @@
 "sbnALT" is used by "sbi2ALT".
 "sbnvOLD" is used by "sbi2vOLD".
 "sbrimALT" is used by "sbiedALT".
+"sbtrt" is used by "sbtr".
 "setrec1lem1" is used by "setrec1lem2".
 "setrec1lem1" is used by "setrec1lem4".
 "setrec1lem1" is used by "setrec2fun".
@@ -12402,6 +13220,14 @@
 "spanval" is used by "spanss".
 "spanval" is used by "spanss2".
 "specval" is used by "speccl".
+"spim" is used by "cbv3".
+"spim" is used by "chvar".
+"spim" is used by "spimv".
+"spime" is used by "exnel".
+"spime" is used by "spimev".
+"spimed" is used by "2ax6elem".
+"spimed" is used by "spime".
+"spimv" is used by "spv".
 "sps-o" is used by "ax12el".
 "sps-o" is used by "ax12eq".
 "sps-o" is used by "ax12inda".
@@ -12410,6 +13236,8 @@
 "sps-o" is used by "axc11n-16".
 "sps-o" is used by "axc5c711toc7".
 "spsbeALT" is used by "sbftALT".
+"spv" is used by "axc11n-16".
+"spv" is used by "cbvalvOLD".
 "sqgt0sr" is used by "recexsr".
 "srhmsubcALTV" is used by "crhmsubcALTV".
 "srhmsubcALTV" is used by "drhmsubcALTV".
@@ -12436,6 +13264,8 @@
 "ssmd2" is used by "atmd2".
 "ssmd2" is used by "mdsymi".
 "ssmd2" is used by "ssdmd1".
+"ssopab2b" is used by "eqopab2b".
+"ssoprab2b" is used by "eqoprab2b".
 "sspba" is used by "minvecolem1".
 "sspba" is used by "minvecolem2".
 "sspba" is used by "minvecolem3".
@@ -13134,12 +13964,22 @@ New usage of "1t1e1ALT" is discouraged (2 uses).
 New usage of "235t711" is discouraged (0 uses).
 New usage of "2atm2atN" is discouraged (0 uses).
 New usage of "2atnelvolN" is discouraged (0 uses).
+New usage of "2ax6e" is discouraged (3 uses).
 New usage of "2ax6eOLD" is discouraged (0 uses).
+New usage of "2ax6elem" is discouraged (2 uses).
 New usage of "2bornot2b" is discouraged (0 uses).
 New usage of "2cnALT" is discouraged (0 uses).
+New usage of "2eu1" is discouraged (4 uses).
 New usage of "2eu1OLD" is discouraged (0 uses).
+New usage of "2eu2" is discouraged (1 uses).
+New usage of "2eu3" is discouraged (0 uses).
 New usage of "2eu3OLD" is discouraged (0 uses).
 New usage of "2eu5OLD" is discouraged (0 uses).
+New usage of "2eu7" is discouraged (1 uses).
+New usage of "2eu8" is discouraged (0 uses).
+New usage of "2euex" is discouraged (1 uses).
+New usage of "2euswap" is discouraged (3 uses).
+New usage of "2exeu" is discouraged (5 uses).
 New usage of "2irrexpqALT" is discouraged (0 uses).
 New usage of "2llnjN" is discouraged (1 uses).
 New usage of "2llnjaN" is discouraged (1 uses).
@@ -13151,6 +13991,8 @@ New usage of "2llnneN" is discouraged (0 uses).
 New usage of "2logb9irrALT" is discouraged (0 uses).
 New usage of "2lplnm2N" is discouraged (0 uses).
 New usage of "2lplnmN" is discouraged (0 uses).
+New usage of "2moex" is discouraged (2 uses).
+New usage of "2moswap" is discouraged (1 uses).
 New usage of "2pm13.193" is discouraged (3 uses).
 New usage of "2pm13.193VD" is discouraged (0 uses).
 New usage of "2pmaplubN" is discouraged (1 uses).
@@ -13163,8 +14005,12 @@ New usage of "2polvalN" is discouraged (8 uses).
 New usage of "2sb5nd" is discouraged (2 uses).
 New usage of "2sb5ndALT" is discouraged (0 uses).
 New usage of "2sb5ndVD" is discouraged (0 uses).
+New usage of "2sb5rf" is discouraged (1 uses).
+New usage of "2sb6rf" is discouraged (0 uses).
 New usage of "2sb6rfOLD" is discouraged (0 uses).
+New usage of "2sb8e" is discouraged (0 uses).
 New usage of "2sbcrexOLD" is discouraged (0 uses).
+New usage of "2sbiev" is discouraged (0 uses).
 New usage of "2uasban" is discouraged (0 uses).
 New usage of "2uasbanh" is discouraged (1 uses).
 New usage of "2uasbanhVD" is discouraged (0 uses).
@@ -13303,7 +14149,9 @@ New usage of "adjsym" is discouraged (5 uses).
 New usage of "adjval" is discouraged (2 uses).
 New usage of "adjval2" is discouraged (0 uses).
 New usage of "adjvalval" is discouraged (1 uses).
+New usage of "aecom" is discouraged (3 uses).
 New usage of "aecom-o" is discouraged (4 uses).
+New usage of "aecoms" is discouraged (13 uses).
 New usage of "aecoms-o" is discouraged (6 uses).
 New usage of "aev-o" is discouraged (1 uses).
 New usage of "aevdemo" is discouraged (0 uses).
@@ -13440,7 +14288,9 @@ New usage of "ax1" is discouraged (0 uses).
 New usage of "ax10fromc7" is discouraged (3 uses).
 New usage of "ax10w" is discouraged (0 uses).
 New usage of "ax11w" is discouraged (0 uses).
+New usage of "ax12" is discouraged (4 uses).
 New usage of "ax12a2-o" is discouraged (0 uses).
+New usage of "ax12b" is discouraged (0 uses).
 New usage of "ax12el" is discouraged (0 uses).
 New usage of "ax12eq" is discouraged (0 uses).
 New usage of "ax12f" is discouraged (0 uses).
@@ -13453,10 +14303,12 @@ New usage of "ax12indi" is discouraged (0 uses).
 New usage of "ax12indn" is discouraged (1 uses).
 New usage of "ax12v2-o" is discouraged (1 uses).
 New usage of "ax12vALT" is discouraged (0 uses).
+New usage of "ax13" is discouraged (4 uses).
 New usage of "ax13ALT" is discouraged (0 uses).
 New usage of "ax13fromc9" is discouraged (0 uses).
 New usage of "ax13lem1" is discouraged (6 uses).
 New usage of "ax13lem2" is discouraged (3 uses).
+New usage of "ax13v" is discouraged (2 uses).
 New usage of "ax1cn" is discouraged (0 uses).
 New usage of "ax1ne0" is discouraged (0 uses).
 New usage of "ax1rid" is discouraged (0 uses).
@@ -13467,6 +14319,8 @@ New usage of "ax4fromc4" is discouraged (0 uses).
 New usage of "ax5ALT" is discouraged (0 uses).
 New usage of "ax5el" is discouraged (1 uses).
 New usage of "ax5eq" is discouraged (1 uses).
+New usage of "ax6" is discouraged (1 uses).
+New usage of "ax6e" is discouraged (27 uses).
 New usage of "ax6e2eq" is discouraged (3 uses).
 New usage of "ax6e2eqVD" is discouraged (0 uses).
 New usage of "ax6e2nd" is discouraged (3 uses).
@@ -13483,6 +14337,9 @@ New usage of "ax9ALT" is discouraged (0 uses).
 New usage of "ax9v" is discouraged (2 uses).
 New usage of "axac2" is discouraged (0 uses).
 New usage of "axacnd" is discouraged (2 uses).
+New usage of "axacndlem1" is discouraged (2 uses).
+New usage of "axacndlem2" is discouraged (2 uses).
+New usage of "axacndlem3" is discouraged (2 uses).
 New usage of "axacndlem4" is discouraged (1 uses).
 New usage of "axacndlem5" is discouraged (1 uses).
 New usage of "axacprim" is discouraged (0 uses).
@@ -13490,16 +14347,23 @@ New usage of "axaddass" is discouraged (0 uses).
 New usage of "axaddcl" is discouraged (0 uses).
 New usage of "axaddf" is discouraged (1 uses).
 New usage of "axaddrcl" is discouraged (0 uses).
+New usage of "axbnd" is discouraged (0 uses).
 New usage of "axbndOLD" is discouraged (0 uses).
+New usage of "axc10" is discouraged (1 uses).
+New usage of "axc11" is discouraged (12 uses).
 New usage of "axc11-o" is discouraged (0 uses).
+New usage of "axc11n" is discouraged (9 uses).
 New usage of "axc11n-16" is discouraged (0 uses).
 New usage of "axc11next" is discouraged (0 uses).
 New usage of "axc11nfromc11" is discouraged (0 uses).
+New usage of "axc14" is discouraged (0 uses).
+New usage of "axc15" is discouraged (5 uses).
 New usage of "axc15OLD" is discouraged (0 uses).
 New usage of "axc16ALT" is discouraged (1 uses).
 New usage of "axc16b" is discouraged (0 uses).
 New usage of "axc16g-o" is discouraged (1 uses).
 New usage of "axc16gALT" is discouraged (0 uses).
+New usage of "axc16i" is discouraged (1 uses).
 New usage of "axc16nfALT" is discouraged (0 uses).
 New usage of "axc4i-o" is discouraged (5 uses).
 New usage of "axc5" is discouraged (0 uses).
@@ -13518,11 +14382,13 @@ New usage of "axc5sp1" is discouraged (0 uses).
 New usage of "axc711" is discouraged (2 uses).
 New usage of "axc711to11" is discouraged (0 uses).
 New usage of "axc711toc7" is discouraged (1 uses).
+New usage of "axc9" is discouraged (12 uses).
 New usage of "axcc" is discouraged (0 uses).
 New usage of "axcnex" is discouraged (0 uses).
 New usage of "axcnre" is discouraged (0 uses).
 New usage of "axdc" is discouraged (0 uses).
 New usage of "axdistr" is discouraged (0 uses).
+New usage of "axextnd" is discouraged (4 uses).
 New usage of "axfrege8" is discouraged (0 uses).
 New usage of "axhcompl-zf" is discouraged (0 uses).
 New usage of "axhfi-zf" is discouraged (0 uses).
@@ -13543,6 +14409,7 @@ New usage of "axhvmul0-zf" is discouraged (0 uses).
 New usage of "axhvmulass-zf" is discouraged (0 uses).
 New usage of "axhvmulid-zf" is discouraged (0 uses).
 New usage of "axi10" is discouraged (0 uses).
+New usage of "axi12" is discouraged (1 uses).
 New usage of "axi12OLD" is discouraged (0 uses).
 New usage of "axi2m1" is discouraged (0 uses).
 New usage of "axi4" is discouraged (0 uses).
@@ -13570,6 +14437,10 @@ New usage of "axnul" is discouraged (0 uses).
 New usage of "axnulALT" is discouraged (0 uses).
 New usage of "axpjcl" is discouraged (7 uses).
 New usage of "axpjpj" is discouraged (8 uses).
+New usage of "axpownd" is discouraged (2 uses).
+New usage of "axpowndlem2" is discouraged (1 uses).
+New usage of "axpowndlem3" is discouraged (1 uses).
+New usage of "axpowndlem4" is discouraged (1 uses).
 New usage of "axpr" is discouraged (0 uses).
 New usage of "axprALT" is discouraged (0 uses).
 New usage of "axpre-ltadd" is discouraged (0 uses).
@@ -13577,6 +14448,12 @@ New usage of "axpre-lttri" is discouraged (0 uses).
 New usage of "axpre-lttrn" is discouraged (0 uses).
 New usage of "axpre-mulgt0" is discouraged (0 uses).
 New usage of "axpre-sup" is discouraged (0 uses).
+New usage of "axregnd" is discouraged (2 uses).
+New usage of "axregndlem1" is discouraged (2 uses).
+New usage of "axregndlem2" is discouraged (1 uses).
+New usage of "axrepnd" is discouraged (2 uses).
+New usage of "axrepndlem1" is discouraged (1 uses).
+New usage of "axrepndlem2" is discouraged (1 uses).
 New usage of "axresscn" is discouraged (2 uses).
 New usage of "axrnegex" is discouraged (0 uses).
 New usage of "axrrecex" is discouraged (0 uses).
@@ -13584,6 +14461,8 @@ New usage of "axsep" is discouraged (0 uses).
 New usage of "axsepgfromrep" is discouraged (1 uses).
 New usage of "axtglowdim2ALTV" is discouraged (0 uses).
 New usage of "axtgupdim2ALTV" is discouraged (0 uses).
+New usage of "axunnd" is discouraged (2 uses).
+New usage of "axunndlem1" is discouraged (1 uses).
 New usage of "baerlem5abmN" is discouraged (0 uses).
 New usage of "baerlem5amN" is discouraged (0 uses).
 New usage of "baerlem5bmN" is discouraged (0 uses).
@@ -14059,16 +14938,75 @@ New usage of "cases2ALT" is discouraged (0 uses).
 New usage of "cayleyhamiltonALT" is discouraged (0 uses).
 New usage of "cba" is discouraged (85 uses).
 New usage of "cbncms" is discouraged (5 uses).
+New usage of "cbv1" is discouraged (2 uses).
+New usage of "cbv1h" is discouraged (1 uses).
+New usage of "cbv2" is discouraged (5 uses).
 New usage of "cbv2OLD" is discouraged (0 uses).
+New usage of "cbv2h" is discouraged (2 uses).
+New usage of "cbv3" is discouraged (4 uses).
+New usage of "cbv3h" is discouraged (0 uses).
+New usage of "cbvab" is discouraged (5 uses).
 New usage of "cbvabvOLD" is discouraged (0 uses).
+New usage of "cbval" is discouraged (5 uses).
+New usage of "cbval2" is discouraged (1 uses).
 New usage of "cbval2OLD" is discouraged (0 uses).
 New usage of "cbval2vOLD" is discouraged (0 uses).
+New usage of "cbval2vv" is discouraged (1 uses).
+New usage of "cbvald" is discouraged (16 uses).
+New usage of "cbvaldva" is discouraged (1 uses).
+New usage of "cbvalv" is discouraged (3 uses).
 New usage of "cbvalvOLD" is discouraged (0 uses).
+New usage of "cbvcsb" is discouraged (0 uses).
+New usage of "cbveu" is discouraged (2 uses).
 New usage of "cbveuALT" is discouraged (0 uses).
+New usage of "cbvex" is discouraged (3 uses).
+New usage of "cbvex2" is discouraged (0 uses).
+New usage of "cbvex2vv" is discouraged (2 uses).
+New usage of "cbvex4v" is discouraged (0 uses).
+New usage of "cbvexd" is discouraged (12 uses).
+New usage of "cbvexdva" is discouraged (1 uses).
 New usage of "cbvexsv" is discouraged (2 uses).
+New usage of "cbvexv" is discouraged (1 uses).
 New usage of "cbvexvOLD" is discouraged (0 uses).
+New usage of "cbviing" is discouraged (1 uses).
+New usage of "cbviinvg" is discouraged (0 uses).
+New usage of "cbviota" is discouraged (2 uses).
+New usage of "cbviotav" is discouraged (0 uses).
+New usage of "cbviung" is discouraged (1 uses).
+New usage of "cbviunvg" is discouraged (0 uses).
+New usage of "cbvmo" is discouraged (1 uses).
+New usage of "cbvmptfg" is discouraged (1 uses).
+New usage of "cbvmptg" is discouraged (1 uses).
+New usage of "cbvmptvg" is discouraged (0 uses).
+New usage of "cbvopab1g" is discouraged (1 uses).
+New usage of "cbvrab" is discouraged (3 uses).
+New usage of "cbvrabcsf" is discouraged (4 uses).
 New usage of "cbvrabvOLD" is discouraged (0 uses).
+New usage of "cbvral" is discouraged (9 uses).
+New usage of "cbvral2v" is discouraged (1 uses).
+New usage of "cbvral3v" is discouraged (0 uses).
+New usage of "cbvralcsf" is discouraged (2 uses).
+New usage of "cbvralf" is discouraged (2 uses).
+New usage of "cbvralsv" is discouraged (0 uses).
+New usage of "cbvralv" is discouraged (8 uses).
+New usage of "cbvralv2" is discouraged (0 uses).
+New usage of "cbvreu" is discouraged (2 uses).
+New usage of "cbvreucsf" is discouraged (0 uses).
+New usage of "cbvreuv" is discouraged (0 uses).
+New usage of "cbvrex" is discouraged (5 uses).
+New usage of "cbvrex2v" is discouraged (0 uses).
+New usage of "cbvrexcsf" is discouraged (1 uses).
 New usage of "cbvrexdva2OLD" is discouraged (0 uses).
+New usage of "cbvrexf" is discouraged (1 uses).
+New usage of "cbvrexsv" is discouraged (1 uses).
+New usage of "cbvrexv" is discouraged (6 uses).
+New usage of "cbvrexv2" is discouraged (0 uses).
+New usage of "cbvriota" is discouraged (1 uses).
+New usage of "cbvriotav" is discouraged (0 uses).
+New usage of "cbvrmo" is discouraged (1 uses).
+New usage of "cbvrmov" is discouraged (0 uses).
+New usage of "cbvsbc" is discouraged (2 uses).
+New usage of "cbvsbcv" is discouraged (0 uses).
 New usage of "ccat2s1fstOLD" is discouraged (0 uses).
 New usage of "ccat2s1fvwALT" is discouraged (0 uses).
 New usage of "ccat2s1fvwALTOLD" is discouraged (0 uses).
@@ -14082,6 +15020,8 @@ New usage of "ccatval1OLD" is discouraged (2 uses).
 New usage of "ccatw2s1assOLD" is discouraged (2 uses).
 New usage of "ccatw2s1ccatws2OLD" is discouraged (1 uses).
 New usage of "ccatw2s1p1OLD" is discouraged (0 uses).
+New usage of "cdeqab1" is discouraged (0 uses).
+New usage of "cdeqal1" is discouraged (0 uses).
 New usage of "cdj1i" is discouraged (0 uses).
 New usage of "cdj3i" is discouraged (0 uses).
 New usage of "cdj3lem1" is discouraged (2 uses).
@@ -14357,9 +15297,12 @@ New usage of "chub1i" is discouraged (18 uses).
 New usage of "chub2" is discouraged (14 uses).
 New usage of "chub2i" is discouraged (24 uses).
 New usage of "chunssji" is discouraged (0 uses).
+New usage of "chvar" is discouraged (7 uses).
+New usage of "chvarv" is discouraged (3 uses).
 New usage of "clel5OLD" is discouraged (0 uses).
 New usage of "cleljustALT" is discouraged (0 uses).
 New usage of "cleljustALT2" is discouraged (0 uses).
+New usage of "clelsb3f" is discouraged (0 uses).
 New usage of "clelsb3fOLD" is discouraged (0 uses).
 New usage of "clelsb3vOLD" is discouraged (0 uses).
 New usage of "cleqfOLD" is discouraged (0 uses).
@@ -14458,16 +15401,21 @@ New usage of "con5i" is discouraged (2 uses).
 New usage of "conventions" is discouraged (0 uses).
 New usage of "conventions-comments" is discouraged (0 uses).
 New usage of "conventions-labels" is discouraged (0 uses).
+New usage of "copsexg" is discouraged (1 uses).
 New usage of "counop" is discouraged (0 uses).
 New usage of "crhmsubcALTV" is discouraged (1 uses).
 New usage of "cringcALTV" is discouraged (9 uses).
 New usage of "cringcatALTV" is discouraged (0 uses).
 New usage of "crngcALTV" is discouraged (7 uses).
 New usage of "csbcnvgALT" is discouraged (0 uses).
+New usage of "csbco" is discouraged (1 uses).
+New usage of "csbco3g" is discouraged (0 uses).
 New usage of "csbeq2gVD" is discouraged (0 uses).
 New usage of "csbfv12gALTVD" is discouraged (0 uses).
 New usage of "csbima12gALTVD" is discouraged (0 uses).
 New usage of "csbingVD" is discouraged (0 uses).
+New usage of "csbnestg" is discouraged (1 uses).
+New usage of "csbnestgf" is discouraged (1 uses).
 New usage of "csbopabgALT" is discouraged (1 uses).
 New usage of "csbresgVD" is discouraged (0 uses).
 New usage of "csbrngVD" is discouraged (0 uses).
@@ -14682,7 +15630,10 @@ New usage of "dfiun2gOLD" is discouraged (0 uses).
 New usage of "dfmo" is discouraged (0 uses).
 New usage of "dfnul2OLD" is discouraged (0 uses).
 New usage of "dfpjop" is discouraged (4 uses).
+New usage of "dfsb1" is discouraged (13 uses).
+New usage of "dfsb2" is discouraged (1 uses).
 New usage of "dfsb2ALT" is discouraged (1 uses).
+New usage of "dfsb3" is discouraged (1 uses).
 New usage of "dfsb3ALT" is discouraged (1 uses).
 New usage of "dfsb7ALT" is discouraged (0 uses).
 New usage of "dfsb7OLD" is discouraged (0 uses).
@@ -14802,6 +15753,7 @@ New usage of "dipfval" is discouraged (3 uses).
 New usage of "diporthcom" is discouraged (1 uses).
 New usage of "dipsubdi" is discouraged (2 uses).
 New usage of "dipsubdir" is discouraged (2 uses).
+New usage of "disjxun" is discouraged (0 uses).
 New usage of "distrlem1pr" is discouraged (1 uses).
 New usage of "distrlem4pr" is discouraged (1 uses).
 New usage of "distrlem5pr" is discouraged (1 uses).
@@ -14860,23 +15812,45 @@ New usage of "dochpolN" is discouraged (0 uses).
 New usage of "dochsordN" is discouraged (0 uses).
 New usage of "dochspocN" is discouraged (0 uses).
 New usage of "domepOLD" is discouraged (0 uses).
+New usage of "dral1" is discouraged (10 uses).
 New usage of "dral1-o" is discouraged (4 uses).
 New usage of "dral1ALT" is discouraged (0 uses).
+New usage of "dral2" is discouraged (7 uses).
 New usage of "dral2-o" is discouraged (4 uses).
+New usage of "drex1" is discouraged (10 uses).
+New usage of "drex2" is discouraged (4 uses).
 New usage of "drhmsubcALTV" is discouraged (1 uses).
+New usage of "drnf1" is discouraged (4 uses).
+New usage of "drnf2" is discouraged (3 uses).
+New usage of "drnfc1" is discouraged (5 uses).
 New usage of "drnfc1OLD" is discouraged (0 uses).
+New usage of "drnfc2" is discouraged (0 uses).
 New usage of "drngcatALTV" is discouraged (0 uses).
 New usage of "drngoi" is discouraged (2 uses).
+New usage of "drsb1" is discouraged (4 uses).
 New usage of "dtruALT" is discouraged (0 uses).
 New usage of "dtruALT2" is discouraged (0 uses).
+New usage of "dtrucor2" is discouraged (0 uses).
 New usage of "dummylink" is discouraged (0 uses).
 New usage of "dvadiaN" is discouraged (1 uses).
+New usage of "dveel1" is discouraged (1 uses).
+New usage of "dveel2" is discouraged (1 uses).
 New usage of "dveel2ALT" is discouraged (0 uses).
+New usage of "dveeq1" is discouraged (2 uses).
 New usage of "dveeq1-o" is discouraged (1 uses).
 New usage of "dveeq1-o16" is discouraged (0 uses).
+New usage of "dveeq2" is discouraged (2 uses).
 New usage of "dveeq2-o" is discouraged (4 uses).
 New usage of "dveeq2ALT" is discouraged (0 uses).
+New usage of "dvelim" is discouraged (3 uses).
+New usage of "dvelimc" is discouraged (1 uses).
+New usage of "dvelimdc" is discouraged (1 uses).
+New usage of "dvelimdf" is discouraged (3 uses).
+New usage of "dvelimf" is discouraged (3 uses).
 New usage of "dvelimf-o" is discouraged (3 uses).
+New usage of "dvelimh" is discouraged (6 uses).
+New usage of "dvelimnf" is discouraged (2 uses).
+New usage of "dvelimv" is discouraged (4 uses).
 New usage of "dvh2dimatN" is discouraged (0 uses).
 New usage of "dvh3dim3N" is discouraged (0 uses).
 New usage of "dvh3dimatN" is discouraged (1 uses).
@@ -15076,6 +16050,7 @@ New usage of "eleigveccl" is discouraged (3 uses).
 New usage of "eleq2dALT" is discouraged (0 uses).
 New usage of "elex22VD" is discouraged (0 uses).
 New usage of "elex2VD" is discouraged (0 uses).
+New usage of "elfvmptrab1" is discouraged (0 uses).
 New usage of "elghomOLD" is discouraged (5 uses).
 New usage of "elghomlem1OLD" is discouraged (1 uses).
 New usage of "elghomlem2OLD" is discouraged (1 uses).
@@ -15101,6 +16076,7 @@ New usage of "elnlfn" is discouraged (4 uses).
 New usage of "elnlfn2" is discouraged (2 uses).
 New usage of "elnp" is discouraged (5 uses).
 New usage of "elnpi" is discouraged (4 uses).
+New usage of "elovmporab1" is discouraged (0 uses).
 New usage of "elpaddatiN" is discouraged (2 uses).
 New usage of "elpaddatriN" is discouraged (0 uses).
 New usage of "elpclN" is discouraged (1 uses).
@@ -15149,6 +16125,8 @@ New usage of "epelgOLD" is discouraged (0 uses).
 New usage of "eqeq1dALT" is discouraged (0 uses).
 New usage of "eqeqan12dALT" is discouraged (0 uses).
 New usage of "eqid1" is discouraged (0 uses).
+New usage of "eqopab2b" is discouraged (1 uses).
+New usage of "eqoprab2b" is discouraged (1 uses).
 New usage of "eqresr" is discouraged (4 uses).
 New usage of "eqsbc3OLD" is discouraged (0 uses).
 New usage of "eqsbc3rVD" is discouraged (0 uses).
@@ -15160,14 +16138,27 @@ New usage of "equidqe" is discouraged (2 uses).
 New usage of "equncomVD" is discouraged (0 uses).
 New usage of "equncomiVD" is discouraged (0 uses).
 New usage of "equs3OLD" is discouraged (0 uses).
+New usage of "equs4" is discouraged (6 uses).
+New usage of "equs45f" is discouraged (2 uses).
+New usage of "equs5" is discouraged (4 uses).
+New usage of "equs5a" is discouraged (2 uses).
 New usage of "equs5aALT" is discouraged (0 uses).
+New usage of "equs5e" is discouraged (1 uses).
 New usage of "equs5eALT" is discouraged (0 uses).
+New usage of "equsal" is discouraged (6 uses).
+New usage of "equsalh" is discouraged (1 uses).
+New usage of "equsb1" is discouraged (6 uses).
 New usage of "equsb1ALT" is discouraged (1 uses).
 New usage of "equsb1vOLD" is discouraged (0 uses).
 New usage of "equsb1vOLDOLD" is discouraged (0 uses).
+New usage of "equsb2" is discouraged (1 uses).
 New usage of "equsb3rOLD" is discouraged (0 uses).
+New usage of "equsex" is discouraged (2 uses).
 New usage of "equsexALT" is discouraged (0 uses).
+New usage of "equsexh" is discouraged (0 uses).
 New usage of "equsexvwOLD" is discouraged (0 uses).
+New usage of "equvel" is discouraged (0 uses).
+New usage of "equvini" is discouraged (1 uses).
 New usage of "equviniOLD" is discouraged (0 uses).
 New usage of "erngbase-rN" is discouraged (4 uses).
 New usage of "erngdv-rN" is discouraged (0 uses).
@@ -15188,6 +16179,8 @@ New usage of "eubiOLD" is discouraged (0 uses).
 New usage of "eubiiOLD" is discouraged (0 uses).
 New usage of "euimOLD" is discouraged (0 uses).
 New usage of "eujustALT" is discouraged (0 uses).
+New usage of "euxfr" is discouraged (0 uses).
+New usage of "euxfr2" is discouraged (1 uses).
 New usage of "ex-decpmul" is discouraged (0 uses).
 New usage of "ex-gt" is discouraged (0 uses).
 New usage of "ex-gte" is discouraged (0 uses).
@@ -15212,6 +16205,7 @@ New usage of "exanOLD" is discouraged (0 uses).
 New usage of "exatleN" is discouraged (1 uses).
 New usage of "exbirVD" is discouraged (0 uses).
 New usage of "exbiriVD" is discouraged (0 uses).
+New usage of "exdistrf" is discouraged (1 uses).
 New usage of "exgenOLD" is discouraged (0 uses).
 New usage of "exidu1" is discouraged (3 uses).
 New usage of "exinst" is discouraged (1 uses).
@@ -15388,6 +16382,8 @@ New usage of "hatomic" is discouraged (1 uses).
 New usage of "hatomici" is discouraged (6 uses).
 New usage of "hatomistici" is discouraged (1 uses).
 New usage of "hba1-o" is discouraged (8 uses).
+New usage of "hbabg" is discouraged (2 uses).
+New usage of "hbae" is discouraged (3 uses).
 New usage of "hbae-o" is discouraged (4 uses).
 New usage of "hbalg" is discouraged (1 uses).
 New usage of "hbalgVD" is discouraged (0 uses).
@@ -15396,10 +16392,18 @@ New usage of "hbexg" is discouraged (0 uses).
 New usage of "hbexgVD" is discouraged (0 uses).
 New usage of "hbimpg" is discouraged (0 uses).
 New usage of "hbimpgVD" is discouraged (0 uses).
+New usage of "hblemg" is discouraged (0 uses).
+New usage of "hbnae" is discouraged (8 uses).
 New usage of "hbnae-o" is discouraged (3 uses).
+New usage of "hbnaes" is discouraged (0 uses).
 New usage of "hbntal" is discouraged (3 uses).
 New usage of "hbra2VD" is discouraged (0 uses).
+New usage of "hbsb" is discouraged (2 uses).
+New usage of "hbsb2" is discouraged (1 uses).
 New usage of "hbsb2ALT" is discouraged (1 uses).
+New usage of "hbsb2a" is discouraged (2 uses).
+New usage of "hbsb2e" is discouraged (0 uses).
+New usage of "hbsb3" is discouraged (2 uses).
 New usage of "hcau" is discouraged (4 uses).
 New usage of "hcaucvg" is discouraged (1 uses).
 New usage of "hcauseq" is discouraged (0 uses).
@@ -15850,6 +16854,7 @@ New usage of "int2" is discouraged (3 uses).
 New usage of "int3" is discouraged (1 uses).
 New usage of "intnatN" is discouraged (0 uses).
 New usage of "iorlid" is discouraged (2 uses).
+New usage of "iotaeq" is discouraged (0 uses).
 New usage of "ip0i" is discouraged (1 uses).
 New usage of "ip1i" is discouraged (2 uses).
 New usage of "ip1ilem" is discouraged (1 uses).
@@ -16332,6 +17337,8 @@ New usage of "mndomgmid" is discouraged (3 uses).
 New usage of "mo4OLD" is discouraged (0 uses).
 New usage of "mobidvALT" is discouraged (0 uses).
 New usage of "mobiiOLD" is discouraged (0 uses).
+New usage of "moexex" is discouraged (2 uses).
+New usage of "moexexv" is discouraged (0 uses).
 New usage of "moimiOLD" is discouraged (0 uses).
 New usage of "mpteq12dvOLD" is discouraged (0 uses).
 New usage of "mptresidOLD" is discouraged (0 uses).
@@ -16374,27 +17381,83 @@ New usage of "mulsrpr" is discouraged (9 uses).
 New usage of "n0lpligALT" is discouraged (0 uses).
 New usage of "n2dvds1OLD" is discouraged (0 uses).
 New usage of "n2dvds3OLD" is discouraged (0 uses).
+New usage of "naecoms" is discouraged (7 uses).
 New usage of "naecoms-o" is discouraged (1 uses).
 New usage of "natded" is discouraged (0 uses).
+New usage of "nd1" is discouraged (5 uses).
+New usage of "nd2" is discouraged (4 uses).
+New usage of "nd4" is discouraged (1 uses).
 New usage of "negexsr" is discouraged (0 uses).
 New usage of "nelbOLD" is discouraged (0 uses).
 New usage of "nelne1OLD" is discouraged (0 uses).
 New usage of "nelne2OLD" is discouraged (0 uses).
 New usage of "nf5rOLD" is discouraged (0 uses).
 New usage of "nfa1-o" is discouraged (4 uses).
+New usage of "nfaba1g" is discouraged (0 uses).
+New usage of "nfabd" is discouraged (5 uses).
+New usage of "nfabd2" is discouraged (3 uses).
 New usage of "nfabd2OLD" is discouraged (0 uses).
 New usage of "nfabdOLD" is discouraged (0 uses).
+New usage of "nfabg" is discouraged (3 uses).
+New usage of "nfae" is discouraged (23 uses).
+New usage of "nfald2" is discouraged (6 uses).
+New usage of "nfccdeq" is discouraged (0 uses).
+New usage of "nfcdeq" is discouraged (1 uses).
 New usage of "nfceqiOLD" is discouraged (0 uses).
+New usage of "nfcsb" is discouraged (6 uses).
+New usage of "nfcsbd" is discouraged (1 uses).
+New usage of "nfcvb" is discouraged (0 uses).
+New usage of "nfcvf" is discouraged (26 uses).
+New usage of "nfcvf2" is discouraged (16 uses).
 New usage of "nfcvfOLD" is discouraged (0 uses).
+New usage of "nfdisj" is discouraged (0 uses).
+New usage of "nfeqf" is discouraged (9 uses).
+New usage of "nfeqf1" is discouraged (7 uses).
+New usage of "nfeqf2" is discouraged (16 uses).
 New usage of "nfequid-o" is discouraged (0 uses).
+New usage of "nfeu" is discouraged (3 uses).
 New usage of "nfeu1ALT" is discouraged (0 uses).
+New usage of "nfeud" is discouraged (1 uses).
+New usage of "nfeud2" is discouraged (2 uses).
+New usage of "nfexd2" is discouraged (1 uses).
+New usage of "nfiing" is discouraged (0 uses).
+New usage of "nfiota" is discouraged (1 uses).
+New usage of "nfiotad" is discouraged (2 uses).
+New usage of "nfiundg" is discouraged (0 uses).
+New usage of "nfiung" is discouraged (0 uses).
+New usage of "nfixp" is discouraged (1 uses).
+New usage of "nfmo" is discouraged (3 uses).
+New usage of "nfmod" is discouraged (2 uses).
+New usage of "nfmod2" is discouraged (5 uses).
+New usage of "nfnae" is discouraged (48 uses).
 New usage of "nfopdALT" is discouraged (0 uses).
+New usage of "nfra2" is discouraged (1 uses).
+New usage of "nfrab" is discouraged (6 uses).
+New usage of "nfral" is discouraged (9 uses).
+New usage of "nfrald" is discouraged (2 uses).
+New usage of "nfreu" is discouraged (0 uses).
+New usage of "nfreud" is discouraged (1 uses).
+New usage of "nfrexdg" is discouraged (2 uses).
+New usage of "nfrexg" is discouraged (1 uses).
+New usage of "nfriotad" is discouraged (0 uses).
+New usage of "nfrmo" is discouraged (0 uses).
+New usage of "nfrmod" is discouraged (0 uses).
+New usage of "nfs1" is discouraged (2 uses).
 New usage of "nfsab1OLD" is discouraged (0 uses).
+New usage of "nfsabg" is discouraged (1 uses).
+New usage of "nfsb" is discouraged (20 uses).
+New usage of "nfsb2" is discouraged (4 uses).
 New usage of "nfsb2ALT" is discouraged (1 uses).
+New usage of "nfsb4" is discouraged (2 uses).
 New usage of "nfsb4ALT" is discouraged (1 uses).
+New usage of "nfsb4t" is discouraged (3 uses).
 New usage of "nfsb4tALT" is discouraged (1 uses).
 New usage of "nfsbOLD" is discouraged (0 uses).
+New usage of "nfsbc" is discouraged (4 uses).
+New usage of "nfsbcd" is discouraged (3 uses).
+New usage of "nfsbd" is discouraged (4 uses).
 New usage of "nfsbvOLD" is discouraged (0 uses).
+New usage of "nfsum" is discouraged (0 uses).
 New usage of "nfunidALT" is discouraged (0 uses).
 New usage of "nfunidALT2" is discouraged (0 uses).
 New usage of "nic-ax" is discouraged (7 uses).
@@ -16714,6 +17777,7 @@ New usage of "onfrALTlem5VD" is discouraged (0 uses).
 New usage of "onsetreclem1" is discouraged (2 uses).
 New usage of "onsetreclem2" is discouraged (1 uses).
 New usage of "onsetreclem3" is discouraged (1 uses).
+New usage of "opabid" is discouraged (2 uses).
 New usage of "opabresidOLD" is discouraged (1 uses).
 New usage of "opelcn" is discouraged (1 uses).
 New usage of "opelopab4" is discouraged (0 uses).
@@ -16722,6 +17786,7 @@ New usage of "opelreal" is discouraged (8 uses).
 New usage of "opidon2OLD" is discouraged (1 uses).
 New usage of "opidonOLD" is discouraged (2 uses).
 New usage of "opnmblALT" is discouraged (0 uses).
+New usage of "oprabid" is discouraged (1 uses).
 New usage of "opreu2reuALT" is discouraged (0 uses).
 New usage of "opsqrlem1" is discouraged (0 uses).
 New usage of "opsqrlem2" is discouraged (1 uses).
@@ -17070,6 +18135,7 @@ New usage of "rabbidvaOLD" is discouraged (0 uses).
 New usage of "ralab2OLD" is discouraged (0 uses).
 New usage of "ralanidOLD" is discouraged (0 uses).
 New usage of "ralbiOLD" is discouraged (0 uses).
+New usage of "ralcom2" is discouraged (1 uses).
 New usage of "ralcom4OLD" is discouraged (0 uses).
 New usage of "raleleqALT" is discouraged (0 uses).
 New usage of "raleqOLD" is discouraged (0 uses).
@@ -17078,6 +18144,7 @@ New usage of "raleqbidvOLD" is discouraged (0 uses).
 New usage of "ralnex2OLD" is discouraged (0 uses).
 New usage of "ralnex3OLD" is discouraged (0 uses).
 New usage of "ralrexbidOLD" is discouraged (0 uses).
+New usage of "ralrnmpt" is discouraged (1 uses).
 New usage of "ralsngOLD" is discouraged (0 uses).
 New usage of "ralxfrALT" is discouraged (0 uses).
 New usage of "rb-ax1" is discouraged (5 uses).
@@ -17146,7 +18213,9 @@ New usage of "rexcomOLD" is discouraged (0 uses).
 New usage of "rexeqOLD" is discouraged (0 uses).
 New usage of "rexeqbi1dvOLD" is discouraged (0 uses).
 New usage of "rexeqbidvOLD" is discouraged (0 uses).
+New usage of "rexrnmpt" is discouraged (0 uses).
 New usage of "rexsngOLD" is discouraged (0 uses).
+New usage of "rgen2a" is discouraged (0 uses).
 New usage of "rhmsubcALTV" is discouraged (1 uses).
 New usage of "rhmsubcALTVcat" is discouraged (0 uses).
 New usage of "rhmsubcALTVlem1" is discouraged (1 uses).
@@ -17241,18 +18310,27 @@ New usage of "rucALT" is discouraged (0 uses).
 New usage of "rusbcALT" is discouraged (0 uses).
 New usage of "s1dmALT" is discouraged (0 uses).
 New usage of "s2dmALT" is discouraged (0 uses).
+New usage of "sb1" is discouraged (5 uses).
+New usage of "sb10f" is discouraged (0 uses).
 New usage of "sb1ALT" is discouraged (4 uses).
 New usage of "sb1OLD" is discouraged (0 uses).
+New usage of "sb2" is discouraged (11 uses).
 New usage of "sb2ALT" is discouraged (7 uses).
+New usage of "sb2ae" is discouraged (0 uses).
 New usage of "sb2vOLD" is discouraged (3 uses).
 New usage of "sb2vOLDALT" is discouraged (1 uses).
 New usage of "sb2vOLDOLD" is discouraged (0 uses).
+New usage of "sb3" is discouraged (2 uses).
 New usage of "sb3OLD" is discouraged (0 uses).
+New usage of "sb3b" is discouraged (2 uses).
 New usage of "sb3bOLD" is discouraged (0 uses).
 New usage of "sb4ALT" is discouraged (4 uses).
 New usage of "sb4OLD" is discouraged (2 uses).
+New usage of "sb4a" is discouraged (2 uses).
 New usage of "sb4aALT" is discouraged (1 uses).
+New usage of "sb4b" is discouraged (13 uses).
 New usage of "sb4bOLD" is discouraged (0 uses).
+New usage of "sb4e" is discouraged (1 uses).
 New usage of "sb4vOLD" is discouraged (2 uses).
 New usage of "sb4vOLDALT" is discouraged (1 uses).
 New usage of "sb4vOLDOLD" is discouraged (0 uses).
@@ -17261,12 +18339,27 @@ New usage of "sb5ALT" is discouraged (0 uses).
 New usage of "sb5ALT2" is discouraged (1 uses).
 New usage of "sb5ALTVD" is discouraged (0 uses).
 New usage of "sb5OLD" is discouraged (0 uses).
+New usage of "sb5f" is discouraged (1 uses).
 New usage of "sb5fALT" is discouraged (1 uses).
+New usage of "sb5rf" is discouraged (0 uses).
 New usage of "sb6ALT" is discouraged (1 uses).
 New usage of "sb6OLD" is discouraged (0 uses).
+New usage of "sb6f" is discouraged (2 uses).
 New usage of "sb6fALT" is discouraged (1 uses).
+New usage of "sb6rf" is discouraged (0 uses).
+New usage of "sb6x" is discouraged (0 uses).
+New usage of "sb7f" is discouraged (2 uses).
 New usage of "sb7fALT" is discouraged (1 uses).
+New usage of "sb7h" is discouraged (0 uses).
+New usage of "sb8" is discouraged (4 uses).
+New usage of "sb8e" is discouraged (5 uses).
+New usage of "sb8eu" is discouraged (3 uses).
+New usage of "sb8iota" is discouraged (0 uses).
+New usage of "sb8mo" is discouraged (1 uses).
+New usage of "sb9" is discouraged (1 uses).
+New usage of "sb9i" is discouraged (0 uses).
 New usage of "sbal1" is discouraged (1 uses).
+New usage of "sbal2" is discouraged (2 uses).
 New usage of "sbal2OLD" is discouraged (0 uses).
 New usage of "sbalOLD" is discouraged (0 uses).
 New usage of "sbanALT" is discouraged (1 uses).
@@ -17286,20 +18379,34 @@ New usage of "sbcbi" is discouraged (2 uses).
 New usage of "sbcbi2OLD" is discouraged (0 uses).
 New usage of "sbcbiVD" is discouraged (0 uses).
 New usage of "sbcbidvOLD" is discouraged (0 uses).
+New usage of "sbcco" is discouraged (3 uses).
+New usage of "sbcco3g" is discouraged (0 uses).
 New usage of "sbcel1vOLD" is discouraged (0 uses).
 New usage of "sbcim2g" is discouraged (2 uses).
 New usage of "sbcim2gVD" is discouraged (0 uses).
+New usage of "sbcnestg" is discouraged (1 uses).
+New usage of "sbcnestgf" is discouraged (2 uses).
+New usage of "sbco" is discouraged (2 uses).
+New usage of "sbco2" is discouraged (6 uses).
 New usage of "sbco2ALT" is discouraged (1 uses).
+New usage of "sbco2d" is discouraged (2 uses).
+New usage of "sbco3" is discouraged (1 uses).
+New usage of "sbcom" is discouraged (0 uses).
+New usage of "sbcom3" is discouraged (3 uses).
 New usage of "sbcoreleleq" is discouraged (2 uses).
 New usage of "sbcoreleleqVD" is discouraged (0 uses).
 New usage of "sbcrexgOLD" is discouraged (2 uses).
 New usage of "sbcssgVD" is discouraged (0 uses).
+New usage of "sbel2x" is discouraged (0 uses).
 New usage of "sbequ12ALT" is discouraged (2 uses).
 New usage of "sbequ1ALT" is discouraged (4 uses).
 New usage of "sbequ1OLD" is discouraged (0 uses).
 New usage of "sbequ2ALT" is discouraged (4 uses).
 New usage of "sbequ2OLD" is discouraged (0 uses).
 New usage of "sbequ2OLDOLD" is discouraged (0 uses).
+New usage of "sbequ5" is discouraged (0 uses).
+New usage of "sbequ6" is discouraged (0 uses).
+New usage of "sbequ8" is discouraged (0 uses).
 New usage of "sbequALT" is discouraged (1 uses).
 New usage of "sbequOLD" is discouraged (0 uses).
 New usage of "sbequiALT" is discouraged (1 uses).
@@ -17308,13 +18415,20 @@ New usage of "sbequivvOLD" is discouraged (1 uses).
 New usage of "sbequvvOLD" is discouraged (0 uses).
 New usage of "sbfALT" is discouraged (2 uses).
 New usage of "sbftALT" is discouraged (1 uses).
+New usage of "sbhb" is discouraged (0 uses).
 New usage of "sbi1ALT" is discouraged (1 uses).
 New usage of "sbi1OLD" is discouraged (0 uses).
 New usage of "sbi1vOLD" is discouraged (1 uses).
 New usage of "sbi2ALT" is discouraged (1 uses).
 New usage of "sbi2vOLD" is discouraged (0 uses).
+New usage of "sbid2" is discouraged (2 uses).
+New usage of "sbid2v" is discouraged (1 uses).
+New usage of "sbidm" is discouraged (0 uses).
+New usage of "sbie" is discouraged (22 uses).
 New usage of "sbieALT" is discouraged (1 uses).
+New usage of "sbied" is discouraged (3 uses).
 New usage of "sbiedALT" is discouraged (1 uses).
+New usage of "sbiedv" is discouraged (1 uses).
 New usage of "sbiedwOLD" is discouraged (0 uses).
 New usage of "sbievOLD" is discouraged (0 uses).
 New usage of "sbimALT" is discouraged (3 uses).
@@ -17331,6 +18445,8 @@ New usage of "sbnvOLD" is discouraged (1 uses).
 New usage of "sbrimALT" is discouraged (1 uses).
 New usage of "sbtALT" is discouraged (0 uses).
 New usage of "sbtT" is discouraged (0 uses).
+New usage of "sbtr" is discouraged (0 uses).
+New usage of "sbtrt" is discouraged (1 uses).
 New usage of "sbtvOLD" is discouraged (0 uses).
 New usage of "scmateALT" is discouraged (0 uses).
 New usage of "seq1hcau" is discouraged (0 uses).
@@ -17484,8 +18600,15 @@ New usage of "spcegvOLD" is discouraged (0 uses).
 New usage of "spcgvOLD" is discouraged (0 uses).
 New usage of "speccl" is discouraged (0 uses).
 New usage of "specval" is discouraged (1 uses).
+New usage of "spei" is discouraged (0 uses).
 New usage of "speimfwALT" is discouraged (0 uses).
+New usage of "spim" is discouraged (3 uses).
+New usage of "spime" is discouraged (2 uses).
+New usage of "spimed" is discouraged (2 uses).
 New usage of "spimehOLD" is discouraged (0 uses).
+New usage of "spimev" is discouraged (0 uses).
+New usage of "spimt" is discouraged (0 uses).
+New usage of "spimv" is discouraged (1 uses).
 New usage of "spimvALT" is discouraged (0 uses).
 New usage of "sps-o" is discouraged (7 uses).
 New usage of "spsbbiOLD" is discouraged (0 uses).
@@ -17493,6 +18616,7 @@ New usage of "spsbeALT" is discouraged (1 uses).
 New usage of "spsbeOLD" is discouraged (0 uses).
 New usage of "spsbeOLDOLD" is discouraged (0 uses).
 New usage of "spsbimvOLD" is discouraged (0 uses).
+New usage of "spv" is discouraged (2 uses).
 New usage of "spvwOLD" is discouraged (0 uses).
 New usage of "sqgt0sr" is discouraged (1 uses).
 New usage of "srhmsubcALTV" is discouraged (4 uses).
@@ -17510,6 +18634,8 @@ New usage of "sshjval3" is discouraged (0 uses).
 New usage of "ssjo" is discouraged (1 uses).
 New usage of "ssmd1" is discouraged (3 uses).
 New usage of "ssmd2" is discouraged (3 uses).
+New usage of "ssopab2b" is discouraged (1 uses).
+New usage of "ssoprab2b" is discouraged (1 uses).
 New usage of "sspba" is discouraged (15 uses).
 New usage of "sspg" is discouraged (1 uses).
 New usage of "sspgval" is discouraged (3 uses).
@@ -17813,7 +18939,12 @@ New usage of "zaddablx" is discouraged (0 uses).
 New usage of "zexALT" is discouraged (1 uses).
 New usage of "zfac" is discouraged (1 uses).
 New usage of "zfcndac" is discouraged (0 uses).
+New usage of "zfcndext" is discouraged (0 uses).
 New usage of "zfcndinf" is discouraged (0 uses).
+New usage of "zfcndpow" is discouraged (0 uses).
+New usage of "zfcndreg" is discouraged (0 uses).
+New usage of "zfcndrep" is discouraged (0 uses).
+New usage of "zfcndun" is discouraged (0 uses).
 New usage of "zfinf" is discouraged (2 uses).
 New usage of "zfpair" is discouraged (1 uses).
 New usage of "zfregs2VD" is discouraged (0 uses).

From 7a26d8eea574db7981d2890b7fcabfe9195d3e74 Mon Sep 17 00:00:00 2001
From: GinoGiotto <73717712+GinoGiotto@users.noreply.github.com>
Date: Sat, 30 Mar 2024 22:27:41 +0100
Subject: [PATCH 3/4] add comments and references, avoid ax-13 from disjxun

---
 discouraged |   10 +-
 set.mm      | 1466 ++++++++++++++++++++++++++++++++-------------------
 2 files changed, 926 insertions(+), 550 deletions(-)

diff --git a/discouraged b/discouraged
index f395138174..a2d7b39cfa 100755
--- a/discouraged
+++ b/discouraged
@@ -3232,7 +3232,6 @@
 "cbvral" is used by "cbvral2".
 "cbvral" is used by "cbvralsv".
 "cbvral" is used by "cbvralv".
-"cbvral" is used by "disjxun".
 "cbvral" is used by "ralrnmpt".
 "cbvral" is used by "smfinf".
 "cbvral" is used by "smfinflem".
@@ -3245,7 +3244,6 @@
 "cbvralv" is used by "bnj1452".
 "cbvralv" is used by "cbvral2v".
 "cbvralv" is used by "cbvral3v".
-"cbvralv" is used by "disjxun".
 "cbvralv" is used by "frgrwopreglem5ALT".
 "cbvralv" is used by "smfsuplem2".
 "cbvralv" is used by "vonicc".
@@ -10181,7 +10179,6 @@
 "nfrab" is used by "smfsupxr".
 "nfral" is used by "bnj1228".
 "nfral" is used by "cbvral2".
-"nfral" is used by "disjxun".
 "nfral" is used by "eliuniincex".
 "nfral" is used by "nfiing".
 "nfral" is used by "nfra2".
@@ -14982,13 +14979,13 @@ New usage of "cbvopab1g" is discouraged (1 uses).
 New usage of "cbvrab" is discouraged (3 uses).
 New usage of "cbvrabcsf" is discouraged (4 uses).
 New usage of "cbvrabvOLD" is discouraged (0 uses).
-New usage of "cbvral" is discouraged (9 uses).
+New usage of "cbvral" is discouraged (8 uses).
 New usage of "cbvral2v" is discouraged (1 uses).
 New usage of "cbvral3v" is discouraged (0 uses).
 New usage of "cbvralcsf" is discouraged (2 uses).
 New usage of "cbvralf" is discouraged (2 uses).
 New usage of "cbvralsv" is discouraged (0 uses).
-New usage of "cbvralv" is discouraged (8 uses).
+New usage of "cbvralv" is discouraged (7 uses).
 New usage of "cbvralv2" is discouraged (0 uses).
 New usage of "cbvreu" is discouraged (2 uses).
 New usage of "cbvreucsf" is discouraged (0 uses).
@@ -15753,7 +15750,6 @@ New usage of "dipfval" is discouraged (3 uses).
 New usage of "diporthcom" is discouraged (1 uses).
 New usage of "dipsubdi" is discouraged (2 uses).
 New usage of "dipsubdir" is discouraged (2 uses).
-New usage of "disjxun" is discouraged (0 uses).
 New usage of "distrlem1pr" is discouraged (1 uses).
 New usage of "distrlem4pr" is discouraged (1 uses).
 New usage of "distrlem5pr" is discouraged (1 uses).
@@ -17433,7 +17429,7 @@ New usage of "nfnae" is discouraged (48 uses).
 New usage of "nfopdALT" is discouraged (0 uses).
 New usage of "nfra2" is discouraged (1 uses).
 New usage of "nfrab" is discouraged (6 uses).
-New usage of "nfral" is discouraged (9 uses).
+New usage of "nfral" is discouraged (8 uses).
 New usage of "nfrald" is discouraged (2 uses).
 New usage of "nfreu" is discouraged (0 uses).
 New usage of "nfreud" is discouraged (1 uses).
diff --git a/set.mm b/set.mm
index 62e7d70489..2c77691fcf 100644
--- a/set.mm
+++ b/set.mm
@@ -20576,7 +20576,8 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
        Had we additionally required ` x ` and ` y ` be distinct, too, this
        theorem would have been a direct consequence of ~ ax-5 .  So essentially
        this theorem states, that a distinct variable condition can be replaced
-       with an inequality between set variables.  (Contributed by NM,
+       with an inequality between set variables.  Preferably, use the version
+       ~ ax13w to avoid the propagation of ~ ax-13 .  (Contributed by NM,
        30-Jun-2016.)  (New usage is discouraged.) $)
     ax13v $p |- ( -. x = y -> ( y = z -> A. x y = z ) ) $=
       ( ax-13 ) ABCD $.
@@ -20598,6 +20599,7 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
     $d x w $.  $d z w $.  $d y w $.
     $( Derive ~ ax-13 from ~ ax13v and Tarski's FOL. This shows that the
        weakening in ~ ax13v is still sufficient for a complete system.
+       Preferably, use the weaker ~ ax13w to avoid the propagation of ~ ax-13 .
        (Contributed by NM, 21-Dec-2015.)  (Proof shortened by Wolf Lammen,
        31-Jan-2018.)  Reduce axiom usage (Revised by Wolf Lammen, 2-Jun-2021.)
        (New usage is discouraged.) $)
@@ -20622,7 +20624,8 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
 
   ${
     $d x z $.
-    $( An equation between setvar is free of any other setvar.  (Contributed by
+    $( An equation between setvar is free of any other setvar.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
        Wolf Lammen, 9-Jun-2019.)  Remove dependency on ~ ax-12 .  (Revised by
        Wolf Lammen, 16-Dec-2022.)  (New usage is discouraged.) $)
     nfeqf2 $p |- ( -. A. x x = y -> F/ x z = y ) $=
@@ -20633,7 +20636,8 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
 
   ${
     $d x z $.
-    $( Quantifier introduction when one pair of variables is distinct.
+    $( Quantifier introduction when one pair of variables is distinct.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 2-Jan-2002.)  (Revised by NM, 20-Jul-2015.)  Remove
        dependency on ~ ax-11 .  (Revised by Wolf Lammen, 8-Sep-2018.)
        (New usage is discouraged.) $)
@@ -20643,7 +20647,8 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
 
   ${
     $d x z $.
-    $( An equation between setvar is free of any other setvar.  (Contributed by
+    $( An equation between setvar is free of any other setvar.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
        Wolf Lammen, 10-Jun-2019.)  (New usage is discouraged.) $)
     nfeqf1 $p |- ( -. A. x x = y -> F/ x y = z ) $=
       ( weq wal wn wnf nfeqf2 equcom nfbii sylib ) ABDAEFCBDZAGBCDZAGABCHLMACBI
@@ -20652,7 +20657,8 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
 
   ${
     $d x z $.
-    $( Quantifier introduction when one pair of variables is distinct.
+    $( Quantifier introduction when one pair of variables is distinct.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 2-Jan-2002.)  Remove dependency on ~ ax-11 .
        (Revised by Wolf Lammen, 8-Sep-2018.)  (New usage is discouraged.) $)
     dveeq1 $p |- ( -. A. x x = y -> ( y = z -> A. x y = z ) ) $=
@@ -20662,7 +20668,8 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
   ${
     $d x w $.  $d y w $.  $d z w $.
     $( A variable is effectively not free in an equality if it is not either of
-       the involved variables. ` F/ ` version of ~ ax-c9 .  (Contributed by
+       the involved variables. ` F/ ` version of ~ ax-c9 .  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
        Mario Carneiro, 6-Oct-2016.)  Remove dependency on ~ ax-11 .  (Revised
        by Wolf Lammen, 6-Sep-2018.)  (New usage is discouraged.) $)
     nfeqf $p |- ( ( -. A. z z = x /\ -. A. z z = y ) -> F/ z x = y ) $=
@@ -20672,9 +20679,10 @@ auxiliary axiom scheme to achieve scheme completeness (i.e. so that all
       MNUFUJUNCBDMNUIUJUHCABDOPRQSTUAUB $.
   $}
 
-  $( Derive set.mm's original ~ ax-c9 from the shorter ~ ax-13 .  (Contributed
-     by NM, 29-Nov-2015.)  (Revised by NM, 24-Dec-2015.)  (Proof shortened by
-     Wolf Lammen, 29-Apr-2018.)  (New usage is discouraged.) $)
+  $( Derive set.mm's original ~ ax-c9 from the shorter ~ ax-13 .  Usage is
+     discouraged to avoid uninformed ~ ax-13 propagation.  (Contributed by NM,
+     29-Nov-2015.)  (Revised by NM, 24-Dec-2015.)  (Proof shortened by Wolf
+     Lammen, 29-Apr-2018.)  (New usage is discouraged.) $)
   axc9 $p |- ( -. A. z z = x -> ( -. A. z z = y
               -> ( x = y -> A. z x = y ) ) ) $=
     ( weq wal wn wi wa nfeqf nf5rd ex ) CADCEFZCBDCEFZABDZNCEGLMHNCABCIJK $.
@@ -20688,9 +20696,10 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
        ~ ax-6 are believed to be theorems of free logic, although the system
        without ~ ax-6 is not complete in free logic.
 
-       It is preferred to use ~ ax6ev when it is sufficient.  (Contributed by
-       NM, 14-May-1993.)  Shortened after ~ ax13lem1 became available.
-       (Revised by Wolf Lammen, 8-Sep-2018.)  (New usage is discouraged.) $)
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .  It
+       is preferred to use ~ ax6ev when it is sufficient.  (Contributed by NM,
+       14-May-1993.)  Shortened after ~ ax13lem1 became available.  (Revised by
+       Wolf Lammen, 8-Sep-2018.)  (New usage is discouraged.) $)
     ax6e $p |- E. x x = y $=
       ( vw weq wex 19.8a wn wi wal ax13lem1 ax6ev equtr eximii syl6com exlimiiv
       19.35i pm2.61i ) ABDZRAEZRAFCBDZRGZSHCUATTAISABCJTRAACDTRHAACKACBLMPNCBKO
@@ -20703,7 +20712,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
      but having two axioms caused some confusion.)
 
      This theorem should be referenced in place of ~ ax-6 so that all proofs
-     can be traced back to ~ ax6v .  When possible, use the weaker ~ ax6v
+     can be traced back to ~ ax6v .  Usage of this theorem is discouraged
+     because it depends on ~ ax-13 .  When possible, use the weaker ~ ax6v
      rather than ~ ax6 since the ~ ax6v derivation is much shorter and requires
      fewer axioms.  (Contributed by NM, 12-Nov-2013.)  (Revised by NM,
      25-Jul-2015.)  (Proof shortened by Wolf Lammen, 4-Feb-2018.)
@@ -20716,14 +20726,17 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
      ~ ax6fromc10 for the rederivation of ~ ax6 from ~ ax-c10 .
 
      Normally, ~ axc10 should be used rather than ~ ax-c10 , except by theorems
-     specifically studying the latter's properties.  (Contributed by NM,
-     5-Aug-1993.)  (Proof modification is discouraged.)
+     specifically studying the latter's properties.  Usage of this theorem has
+     been discouraged later on to avoid ~ ax-13 propagation.  Check out
+     ~ bj-axc10v for a weaker version requiring less axioms.  (Contributed by
+     NM, 5-Aug-1993.)  (Proof modification is discouraged.)
      (New usage is discouraged.) $)
   axc10 $p |- ( A. x ( x = y -> A. x ph ) -> ph ) $=
     ( weq wal wi wn ax6 con3 al2imi mtoi axc7 syl ) BCDZABEZFZBEZOGZBEZGAQSNGZB
     EBCHPRTBNOIJKABLM $.
 
-  $( Closed theorem form of ~ spim .  (Contributed by NM, 15-Jan-2008.)
+  $( Closed theorem form of ~ spim .  Usage of this theorem is discouraged
+     because it depends on ~ ax-13 .  (Contributed by NM, 15-Jan-2008.)
      (Revised by Mario Carneiro, 17-Oct-2016.)  (Proof shortened by Wolf
      Lammen, 21-Mar-2023.)  (New usage is discouraged.) $)
   spimt $p |- ( ( F/ x ps /\ A. x ( x = y -> ( ph -> ps ) ) ) ->
@@ -20736,9 +20749,11 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     spim.2 $e |- ( x = y -> ( ph -> ps ) ) $.
     $( Specialization, using implicit substitution.  Compare Lemma 14 of
        [Tarski] p. 70.  The ~ spim series of theorems requires that only one
-       direction of the substitution hypothesis hold.  (Contributed by NM,
-       10-Jan-1993.)  (Revised by Mario Carneiro, 3-Oct-2016.)  (Proof
-       shortened by Wolf Lammen, 18-Feb-2018.)  (New usage is discouraged.) $)
+       direction of the substitution hypothesis hold.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Check out ~ spimw for a
+       version requiring less axioms.  (Contributed by NM, 10-Jan-1993.)
+       (Revised by Mario Carneiro, 3-Oct-2016.)  (Proof shortened by Wolf
+       Lammen, 18-Feb-2018.)  (New usage is discouraged.) $)
     spim $p |- ( A. x ph -> ps ) $=
       ( weq wi ax6e eximii 19.36i ) ABCECDGABHCCDIFJK $.
   $}
@@ -20746,9 +20761,11 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
   ${
     spimed.1 $e |- ( ch -> F/ x ph ) $.
     spimed.2 $e |- ( x = y -> ( ph -> ps ) ) $.
-    $( Deduction version of ~ spime .  See also ~ spimedv .  (Contributed by
-       NM, 14-May-1993.)  (Revised by Mario Carneiro, 3-Oct-2016.)  (Proof
-       shortened by Wolf Lammen, 19-Feb-2018.)  (New usage is discouraged.) $)
+    $( Deduction version of ~ spime .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ spimedv if possible.
+       (Contributed by NM, 14-May-1993.)  (Revised by Mario Carneiro,
+       3-Oct-2016.)  (Proof shortened by Wolf Lammen, 19-Feb-2018.)
+       (New usage is discouraged.) $)
     spimed $p |- ( ch -> ( ph -> E. x ps ) ) $=
       ( wal wex nf5rd weq wi ax6e eximii 19.35i syl6 ) CAADHBDICADFJABDDEKABLDD
       EMGNOP $.
@@ -20758,7 +20775,9 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     spime.1 $e |- F/ x ph $.
     spime.2 $e |- ( x = y -> ( ph -> ps ) ) $.
     $( Existential introduction, using implicit substitution.  Compare Lemma 14
-       of [Tarski] p. 70.  (Contributed by NM, 7-Aug-1994.)  (Revised by Mario
+       of [Tarski] p. 70.  Usage of this theorem is discouraged because it
+       depends on ~ ax-13 .  Check out ~ spimew for a weaker version requiring
+       less axioms.  (Contributed by NM, 7-Aug-1994.)  (Revised by Mario
        Carneiro, 3-Oct-2016.)  (Proof shortened by Wolf Lammen, 6-Mar-2018.)
        (New usage is discouraged.) $)
     spime $p |- ( ph -> E. x ps ) $=
@@ -20769,7 +20788,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     $d x ps $.
     spimv.1 $e |- ( x = y -> ( ph -> ps ) ) $.
     $( A version of ~ spim with a distinct variable requirement instead of a
-       bound-variable hypothesis.  See ~ spimfv and ~ spimvw for versions
+       bound-variable hypothesis.  Usage of this theorem is discouraged because
+       it depends on ~ ax-13 .  See ~ spimfv and ~ spimvw for versions
        requiring fewer axioms.  (Contributed by NM, 31-Jul-1993.)
        (New usage is discouraged.) $)
     spimv $p |- ( A. x ph -> ps ) $=
@@ -20788,8 +20808,10 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
   ${
     $d x ph $.
     spimev.1 $e |- ( x = y -> ( ph -> ps ) ) $.
-    $( Distinct-variable version of ~ spime .  (Contributed by NM,
-       10-Jan-1993.)  (New usage is discouraged.) $)
+    $( Distinct-variable version of ~ spime .  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ spimevw if
+       possible.  (Contributed by NM, 10-Jan-1993.)
+       (New usage is discouraged.) $)
     spimev $p |- ( ph -> E. x ps ) $=
       ( nfv spime ) ABCDACFEG $.
   $}
@@ -20797,8 +20819,9 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
   ${
     $d x ps $.
     spv.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( Specialization, using implicit substitution.  See ~ spvv for a version
-       using fewer axioms.  (Contributed by NM, 30-Aug-1993.)
+    $( Specialization, using implicit substitution.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ spvv if
+       possible.  (Contributed by NM, 30-Aug-1993.)
        (New usage is discouraged.) $)
     spv $p |- ( A. x ph -> ps ) $=
       ( weq biimpd spimv ) ABCDCDFABEGH $.
@@ -20808,9 +20831,10 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     spei.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
     spei.2 $e |- ps $.
     $( Inference from existential specialization, using implicit substitution.
-       Remove a distinct variable constraint.  (Contributed by NM,
-       19-Aug-1993.)  (Proof shortened by Wolf Lammen, 12-May-2018.)
-       (New usage is discouraged.) $)
+       Remove a distinct variable constraint.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ speiv if
+       possible.  (Contributed by NM, 19-Aug-1993.)  (Proof shortened by Wolf
+       Lammen, 12-May-2018.)  (New usage is discouraged.) $)
     spei $p |- E. x ph $=
       ( weq ax6e mpbiri eximii ) CDGZACCDHKABFEIJ $.
   $}
@@ -20819,9 +20843,10 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     chvar.1 $e |- F/ x ps $.
     chvar.2 $e |- ( x = y -> ( ph <-> ps ) ) $.
     chvar.3 $e |- ph $.
-    $( Implicit substitution of ` y ` for ` x ` into a theorem.  (Contributed
-       by Raph Levien, 9-Jul-2003.)  (Revised by Mario Carneiro, 3-Oct-2016.)
-       (New usage is discouraged.) $)
+    $( Implicit substitution of ` y ` for ` x ` into a theorem.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  Use the weaker
+       ~ chvarfv if possible.  (Contributed by Raph Levien, 9-Jul-2003.)
+       (Revised by Mario Carneiro, 3-Oct-2016.)  (New usage is discouraged.) $)
     chvar $p |- ps $=
       ( weq biimpd spim mpg ) ABCABCDECDHABFIJGK $.
   $}
@@ -20830,9 +20855,10 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     $d x ps $.
     chvarv.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
     chvarv.2 $e |- ph $.
-    $( Implicit substitution of ` y ` for ` x ` into a theorem.  (Contributed
-       by NM, 20-Apr-1994.)  (Proof shortened by Wolf Lammen, 22-Apr-2018.)
-       (New usage is discouraged.) $)
+    $( Implicit substitution of ` y ` for ` x ` into a theorem.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  Use the weaker
+       ~ chvarvv if possible.  (Contributed by NM, 20-Apr-1994.)  (Proof
+       shortened by Wolf Lammen, 22-Apr-2018.)  (New usage is discouraged.) $)
     chvarv $p |- ps $=
       ( nfv chvar ) ABCDBCGEFH $.
   $}
@@ -20842,8 +20868,10 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbv3.2 $e |- F/ x ps $.
     cbv3.3 $e |- ( x = y -> ( ph -> ps ) ) $.
     $( Rule used to change bound variables, using implicit substitution, that
-       does not use ~ ax-c9 .  (Contributed by NM, 5-Aug-1993.)  (Proof
-       shortened by Wolf Lammen, 12-May-2018.)  (New usage is discouraged.) $)
+       does not use ~ ax-c9 .  Usage of this theorem is discouraged because it
+       depends on ~ ax-13 .  Use the weaker ~ cbv3v if possible.  (Contributed
+       by NM, 5-Aug-1993.)  (Proof shortened by Wolf Lammen, 12-May-2018.)
+       (New usage is discouraged.) $)
     cbv3 $p |- ( A. x ph -> A. y ps ) $=
       ( wal nf5ri hbal spim alrimih ) ACHBDADCADEIJABCDFGKL $.
   $}
@@ -20852,18 +20880,19 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbval.1 $e |- F/ y ph $.
     cbval.2 $e |- F/ x ps $.
     cbval.3 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.  See
-       ~ cbvalv , ~ cbvalv1 , and ~ cbvalvw for weaker versions.  The latter
-       two use fewer axioms.  (Contributed by NM, 13-May-1993.)  (Revised by
-       Mario Carneiro, 3-Oct-2016.)  (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Check
+       out ~ cbvalw , ~ cbvalvw , ~ cbvalv1 for versions requiring fewer
+       axioms.  (Contributed by NM, 13-May-1993.)  (Revised by Mario Carneiro,
+       3-Oct-2016.)  (New usage is discouraged.) $)
     cbval $p |- ( A. x ph <-> A. y ps ) $=
       ( wal weq biimpd cbv3 wi biimprd equcoms impbii ) ACHBDHABCDEFCDIZABGJKBA
       DCFEBALCDPABGMNKO $.
 
-    $( Rule used to change bound variables, using implicit substitution.  See
-       ~ cbvexv , ~ cbvexv1 , and ~ cbvexvw for weaker versions.  The latter
-       two use fewer axioms.  (Contributed by NM, 21-Jun-1993.)
-       (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Check
+       out ~ cbvexvw , ~ cbvexv1 for weaker versions requiring fewer axioms.
+       (Contributed by NM, 21-Jun-1993.)  (New usage is discouraged.) $)
     cbvex $p |- ( E. x ph <-> E. y ps ) $=
       ( wex wn wal nfn weq notbid cbval alnex 3bitr3i con4bii ) ACHZBDHZAIZCJBI
       ZDJRISITUACDADEKBCFKCDLABGMNACOBDOPQ $.
@@ -20872,7 +20901,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
   ${
     $d y ph $.  $d x ps $.
     cbvalv.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.  See
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  See
        ~ cbvalvw for a version requiring fewer axioms, to be preferred when
        sufficient.  (Contributed by NM, 5-Aug-1993.)  Remove dependency on
        ~ ax-10 , shorten.  (Revised by Wolf Lammen, 11-Sep-2023.)
@@ -20880,7 +20910,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbvalv $p |- ( A. x ph <-> A. y ps ) $=
       ( nfv cbval ) ABCDADFBCFEG $.
 
-    $( Rule used to change bound variables, using implicit substitution.  See
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  See
        ~ cbvexvw for a version requiring fewer axioms, to be preferred when
        sufficient.  (Contributed by NM, 21-Jun-1993.)  Remove dependency on
        ~ ax-10 , shorten.  (Revised by Wolf Lammen, 11-Sep-2023.)
@@ -20911,7 +20942,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbv1.3 $e |- ( ph -> F/ y ps ) $.
     cbv1.4 $e |- ( ph -> F/ x ch ) $.
     cbv1.5 $e |- ( ph -> ( x = y -> ( ps -> ch ) ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.  See
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  See
        ~ cbv1v with disjoint variable conditions, not depending on ~ ax-13 .
        (Contributed by NM, 5-Aug-1993.)  (Revised by Mario Carneiro,
        3-Oct-2016.)  Format hypotheses to common style.  (Revised by Wolf
@@ -20927,7 +20959,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbv2.3 $e |- ( ph -> F/ y ps ) $.
     cbv2.4 $e |- ( ph -> F/ x ch ) $.
     cbv2.5 $e |- ( ph -> ( x = y -> ( ps <-> ch ) ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.  See
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  See
        ~ cbv2w with disjoint variable conditions, not depending on ~ ax-13 .
        (Contributed by NM, 5-Aug-1993.)  (Revised by Mario Carneiro,
        3-Oct-2016.)  Format hypotheses to common style, avoid ~ ax-10 .
@@ -20942,10 +20975,11 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbv3h.1 $e |- ( ph -> A. y ph ) $.
     cbv3h.2 $e |- ( ps -> A. x ps ) $.
     cbv3h.3 $e |- ( x = y -> ( ph -> ps ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 8-Jun-1993.)  (Proof shortened by Andrew Salmon,
-       25-May-2011.)  (Proof shortened by Wolf Lammen, 12-May-2018.)
-       (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ cbv3hv if possible.  (Contributed by NM, 8-Jun-1993.)  (Proof
+       shortened by Andrew Salmon, 25-May-2011.)  (Proof shortened by Wolf
+       Lammen, 12-May-2018.)  (New usage is discouraged.) $)
     cbv3h $p |- ( A. x ph -> A. y ps ) $=
       ( nf5i cbv3 ) ABCDADEHBCFHGI $.
   $}
@@ -20954,7 +20988,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbv1h.1 $e |- ( ph -> ( ps -> A. y ps ) ) $.
     cbv1h.2 $e |- ( ph -> ( ch -> A. x ch ) ) $.
     cbv1h.3 $e |- ( ph -> ( x = y -> ( ps -> ch ) ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 11-May-1993.)  (Proof shortened by Wolf Lammen,
        13-May-2018.)  (New usage is discouraged.) $)
     cbv1h $p |- ( A. x A. y ph -> ( A. x ps -> A. y ch ) ) $=
@@ -20966,7 +21001,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbv2h.1 $e |- ( ph -> ( ps -> A. y ps ) ) $.
     cbv2h.2 $e |- ( ph -> ( ch -> A. x ch ) ) $.
     cbv2h.3 $e |- ( ph -> ( x = y -> ( ps <-> ch ) ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 11-May-1993.)  (New usage is discouraged.) $)
     cbv2h $p |- ( A. x A. y ph -> ( A. x ps <-> A. y ch ) ) $=
       ( wal weq wb wi biimp syl6 cbv1h equcomi biimpr syl56 alcoms impbid ) AEI
@@ -20995,8 +21031,9 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbvald.2 $e |- ( ph -> F/ y ps ) $.
     cbvald.3 $e |- ( ph -> ( x = y -> ( ps <-> ch ) ) ) $.
     $( Deduction used to change bound variables, using implicit substitution,
-       particularly useful in conjunction with ~ dvelim .  See ~ cbvaldw for a
-       version with ` x , y ` disjoint, not depending on ~ ax-13 .
+       particularly useful in conjunction with ~ dvelim .  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  See ~ cbvaldw
+       for a version with ` x , y ` disjoint, not depending on ~ ax-13 .
        (Contributed by NM, 2-Jan-2002.)  (Revised by Mario Carneiro,
        6-Oct-2016.)  (Revised by Wolf Lammen, 13-May-2018.)
        (New usage is discouraged.) $)
@@ -21004,9 +21041,10 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
       ( nfv nfvd cbv2 ) ABCDEADIFGACDJHK $.
 
     $( Deduction used to change bound variables, using implicit substitution,
-       particularly useful in conjunction with ~ dvelim .  See also ~ cbvexdw .
-       (Contributed by NM, 2-Jan-2002.)  (Revised by Mario Carneiro,
-       6-Oct-2016.)  (New usage is discouraged.) $)
+       particularly useful in conjunction with ~ dvelim .  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  Use the weaker
+       ~ cbvexdw if possible.  (Contributed by NM, 2-Jan-2002.)  (Revised by
+       Mario Carneiro, 6-Oct-2016.)  (New usage is discouraged.) $)
     cbvexd $p |- ( ph -> ( E. x ps <-> E. y ch ) ) $=
       ( wex wn wal nfnd weq wb notbi syl6ib cbvald alnex 3bitr3g con4bid ) ABDI
       ZCEIZABJZDKCJZEKUAJUBJAUCUDDEFABEGLADEMBCNUCUDNHBCOPQBDRCERST $.
@@ -21016,15 +21054,17 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     $d ps y $.  $d ch x $.  $d ph x $.  $d ph y $.
     cbvaldva.1 $e |- ( ( ph /\ x = y ) -> ( ps <-> ch ) ) $.
     $( Rule used to change the bound variable in a universal quantifier with
-       implicit substitution.  Deduction form.  See also ~ cbvaldvaw .
-       (Contributed by David Moews, 1-May-2017.)
+       implicit substitution.  Deduction form.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ cbvaldvaw
+       if possible.  (Contributed by David Moews, 1-May-2017.)
        (New usage is discouraged.) $)
     cbvaldva $p |- ( ph -> ( A. x ps <-> A. y ch ) ) $=
       ( nfv nfvd weq wb ex cbvald ) ABCDEAEGABEHADEIBCJFKL $.
 
     $( Rule used to change the bound variable in an existential quantifier with
-       implicit substitution.  Deduction form.  See also ~ cbvexdvaw .
-       (Contributed by David Moews, 1-May-2017.)
+       implicit substitution.  Deduction form.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ cbvexdvaw
+       if possible.  (Contributed by David Moews, 1-May-2017.)
        (New usage is discouraged.) $)
     cbvexdva $p |- ( ph -> ( E. x ps <-> E. y ch ) ) $=
       ( nfv nfvd weq wb ex cbvexd ) ABCDEAEGABEHADEIBCJFKL $.
@@ -21037,10 +21077,11 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     cbval2.3 $e |- F/ x ps $.
     cbval2.4 $e |- F/ y ps $.
     cbval2.5 $e |- ( ( x = z /\ y = w ) -> ( ph <-> ps ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 22-Dec-2003.)  (Revised by Mario Carneiro,
-       6-Oct-2016.)  (Proof shortened by Wolf Lammen, 11-Sep-2023.)
-       (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ cbval2v if possible.  (Contributed by NM, 22-Dec-2003.)
+       (Revised by Mario Carneiro, 6-Oct-2016.)  (Proof shortened by Wolf
+       Lammen, 11-Sep-2023.)  (New usage is discouraged.) $)
     cbval2 $p |- ( A. x A. y ph <-> A. z A. w ps ) $=
       ( wal nfal weq nfv wnf a1i wb ex cbv2 cbval ) ADLBFLCEAEDGMBCFIMCENZABDFU
       BDOUBFOAFPUBHQBDPUBJQUBDFNABRKSTUA $.
@@ -21054,10 +21095,11 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
       expcom ) ADLZBFLZCEAEDGMBCFIMCENZUEUFUGAOZDLUGBOZFLUGUEOUGUFOUHUIDFUGAFUG
       FPHQUGBDUGDPJQDFNZUGABUGUJABRKUDUASUGADTUGBFTUBUCS $.
 
-    $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 14-Sep-2003.)  (Revised by Mario Carneiro,
-       6-Oct-2016.)  (Proof shortened by Wolf Lammen, 16-Jun-2019.)
-       (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ cbvex2v if possible.  (Contributed by NM, 14-Sep-2003.)
+       (Revised by Mario Carneiro, 6-Oct-2016.)  (Proof shortened by Wolf
+       Lammen, 16-Jun-2019.)  (New usage is discouraged.) $)
     cbvex2 $p |- ( E. x E. y ph <-> E. z E. w ps ) $=
       ( wex wn wal nfn weq wa notbid cbval2 2nexaln 3bitr4i con4bii ) ADLCLZBFL
       ELZAMZDNCNBMZFNENUCMUDMUEUFCDEFAEGOAFHOBCIOBDJOCEPDFPQABKRSACDTBEFTUAUB
@@ -21067,15 +21109,19 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
   ${
     $d z w ph $.  $d x y ps $.  $d x w $.  $d z y $.
     cbval2vv.1 $e |- ( ( x = z /\ y = w ) -> ( ph <-> ps ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 4-Feb-2005.)  Remove dependency on ~ ax-10 .
-       (Revised by Wolf Lammen, 18-Jul-2021.)  (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ cbval2vw if possible.  (Contributed by NM, 4-Feb-2005.)  Remove
+       dependency on ~ ax-10 .  (Revised by Wolf Lammen, 18-Jul-2021.)
+       (New usage is discouraged.) $)
     cbval2vv $p |- ( A. x A. y ph <-> A. z A. w ps ) $=
       ( wal weq cbvaldva cbvalv ) ADHBFHCECEIABDFGJK $.
 
-    $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 26-Jul-1995.)  Remove dependency on ~ ax-10 .
-       (Revised by Wolf Lammen, 18-Jul-2021.)  (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ cbvex2vw if possible.  (Contributed by NM, 26-Jul-1995.)
+       Remove dependency on ~ ax-10 .  (Revised by Wolf Lammen, 18-Jul-2021.)
+       (New usage is discouraged.) $)
     cbvex2vv $p |- ( E. x E. y ph <-> E. z E. w ps ) $=
       ( wex weq cbvexdva cbvexv ) ADHBFHCECEIABDFGJK $.
   $}
@@ -21090,8 +21136,10 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
     $d g z $.  $d u v w z $.  $d u w x z $.  $d v w y z $.  $d w x y z $.
     cbvex4v.1 $e |- ( ( x = v /\ y = u ) -> ( ph <-> ps ) ) $.
     cbvex4v.2 $e |- ( ( z = f /\ w = g ) -> ( ps <-> ch ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 26-Jul-1995.)  (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ cbvex4vw if possible.  (Contributed by NM, 26-Jul-1995.)
+       (New usage is discouraged.) $)
     cbvex4v $p |- ( E. x E. y E. z E. w ph <-> E. v E. u E. f E. g ch ) $=
       ( wex weq wa 2exbidv cbvex2vv 2exbii bitri ) AGNFNZENDNBGNFNZINHNCKNJNZIN
       HNUAUBDEHIDHOEIOPABFGLQRUBUCHIBCFGJKMRST $.
@@ -21099,7 +21147,8 @@ theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10).  In the
 
   $( Lemma used in proofs of implicit substitution properties.  The converse
      requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
-     hypothesis ( ~ equs45f ).  See ~ equs4v for a version requiring fewer
+     hypothesis ( ~ equs45f ).  Usage of this theorem is discouraged because it
+     depends on ~ ax-13 .  See ~ equs4v for a weaker version requiring fewer
      axioms.  (Contributed by NM, 10-May-1993.)  (Proof shortened by Mario
      Carneiro, 20-May-2014.)  (Proof shortened by Wolf Lammen, 5-Feb-2018.)
      (New usage is discouraged.) $)
@@ -21109,7 +21158,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   ${
     equsal.1 $e |- F/ x ps $.
     equsal.2 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( An equivalence related to implicit substitution.  See ~ equsalvw and
+    $( An equivalence related to implicit substitution.  Usage of this theorem
+       is discouraged because it depends on ~ ax-13 .  See ~ equsalvw and
        ~ equsalv for versions with disjoint variable conditions proved from
        fewer axioms.  See also the dual form ~ equsex .  (Contributed by NM,
        2-Jun-1993.)  (Proof shortened by Andrew Salmon, 12-Aug-2011.)  (Revised
@@ -21119,7 +21169,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
       ( weq wi wal wex 19.23 pm5.74i albii ax6e a1bi 3bitr4i ) CDGZBHZCIQCJZBHQ
       AHZCIBQBCEKTRCQABFLMSBCDNOP $.
 
-    $( An equivalence related to implicit substitution.  See ~ equsexvw and
+    $( An equivalence related to implicit substitution.  Usage of this theorem
+       is discouraged because it depends on ~ ax-13 .  See ~ equsexvw and
        ~ equsexv for versions with disjoint variable conditions proved from
        fewer axioms.  See also the dual form ~ equsal .  See ~ equsexALT for an
        alternate proof.  (Contributed by NM, 5-Aug-1993.)  (Revised by Mario
@@ -21145,13 +21196,15 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   ${
     equsalh.1 $e |- ( ps -> A. x ps ) $.
     equsalh.2 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( An equivalence related to implicit substitution.  See ~ equsalhw for a
+    $( An equivalence related to implicit substitution.  Usage of this theorem
+       is discouraged because it depends on ~ ax-13 .  See ~ equsalhw for a
        version with a disjoint variable condition requiring fewer axioms.
        (Contributed by NM, 2-Jun-1993.)  (New usage is discouraged.) $)
     equsalh $p |- ( A. x ( x = y -> ph ) <-> ps ) $=
       ( nf5i equsal ) ABCDBCEGFH $.
 
-    $( An equivalence related to implicit substitution.  See ~ equsexhv for a
+    $( An equivalence related to implicit substitution.  Usage of this theorem
+       is discouraged because it depends on ~ ax-13 .  See ~ equsexhv for a
        version with a disjoint variable condition which does not require
        ~ ax-13 .  (Contributed by NM, 5-Aug-1993.)
        (New usage is discouraged.) $)
@@ -21167,7 +21220,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
        Theorem ~ ax12 shows the reverse derivation of ~ ax-12 from ~ ax-c15 .
 
        Normally, ~ axc15 should be used rather than ~ ax-c15 , except by
-       theorems specifically studying the latter's properties.  (Contributed by
+       theorems specifically studying the latter's properties.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
        NM, 2-Feb-2007.)  (Proof shortened by Wolf Lammen, 26-Mar-2023.)
        (New usage is discouraged.) $)
     axc15 $p |- ( -. A. x x = y ->
@@ -21189,15 +21243,17 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   $}
 
   $( Rederivation of axiom ~ ax-12 from ~ ax12v (used only via ~ sp ) ,
-     ~ axc11r , and ~ axc15 (on top of Tarski's FOL).  (Contributed by NM,
-     22-Jan-2007.)  Proof uses contemporary axioms.  (Revised by Wolf Lammen,
-     8-Aug-2020.)  (Proof shortened by BJ, 4-Jul-2021.)
-     (New usage is discouraged.) $)
+     ~ axc11r , and ~ axc15 (on top of Tarski's FOL).  Since this version
+     depends on ~ ax-13 , usage of the weaker ~ ax12v or ~ ax12w are preferred.
+     (Contributed by NM, 22-Jan-2007.)  Proof uses contemporary axioms.
+     (Revised by Wolf Lammen, 8-Aug-2020.)  (Proof shortened by BJ,
+     4-Jul-2021.)  (New usage is discouraged.) $)
   ax12 $p |- ( x = y -> ( A. y ph -> A. x ( x = y -> ph ) ) ) $=
     ( weq wal wi axc11r ala1 syl6 a1d wn sp axc15 syl7 pm2.61i ) BCDZBEZPACEZPA
     FBEZFZFQTPQRABESACBGAPBHIJRAQKPSACLABCMNO $.
 
-  $( A bidirectional version of ~ axc15 .  (Contributed by NM, 30-Jun-2006.)
+  $( A bidirectional version of ~ axc15 .  Usage of this theorem is discouraged
+     because it depends on ~ ax-13 .  (Contributed by NM, 30-Jun-2006.)
      (New usage is discouraged.) $)
   ax12b $p |- ( ( -. A. x x = y /\ x = y ) ->
               ( ph <-> A. x ( x = y -> ph ) ) ) $=
@@ -21219,6 +21275,7 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
        in [Megill] p. 445 (p. 12 of the preprint).  If a disjoint variable
        condition is added on ` x ` and ` y ` , then this becomes an instance of
        ~ aevlem .  Use ~ aecom instead when this does not lengthen the proof.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 10-May-1993.)  (Revised by NM, 7-Nov-2015.)  (Proof
        shortened by Wolf Lammen, 6-Mar-2018.)  (Revised by Wolf Lammen,
        30-Nov-2019.)  (Proof shortened by BJ, 29-Mar-2021.)  (Proof shortened
@@ -21230,14 +21287,16 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
   $( Commutation law for identical variable specifiers.  Both sides of the
      biconditional are true when ` x ` and ` y ` are substituted with the same
-     variable.  (Contributed by NM, 10-May-1993.)  Change to a biconditional.
+     variable.  Usage of this theorem is discouraged because it depends on
+     ~ ax-13 .  (Contributed by NM, 10-May-1993.)  Change to a biconditional.
      (Revised by BJ, 26-Sep-2019.)  (New usage is discouraged.) $)
   aecom $p |- ( A. x x = y <-> A. y y = x ) $=
     ( weq wal axc11n impbii ) ABCADBACBDABEBAEF $.
 
   ${
     aecoms.1 $e |- ( A. x x = y -> ph ) $.
-    $( A commutation rule for identical variable specifiers.  (Contributed by
+    $( A commutation rule for identical variable specifiers.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
        NM, 10-May-1993.)  (New usage is discouraged.) $)
     aecoms $p |- ( A. y y = x -> ph ) $=
       ( weq wal aecom sylbi ) CBECFBCEBFACBGDH $.
@@ -21245,7 +21304,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
   ${
     naecoms.1 $e |- ( -. A. x x = y -> ph ) $.
-    $( A commutation rule for distinct variable specifiers.  (Contributed by
+    $( A commutation rule for distinct variable specifiers.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
        NM, 2-Jan-2002.)  (New usage is discouraged.) $)
     naecoms $p |- ( -. A. y y = x -> ph ) $=
       ( weq wal aecom sylnbir ) CBECFBCEBFABCGDH $.
@@ -21253,42 +21313,49 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
   $( Show that ~ ax-c11 can be derived from ~ ax-c11n in the form of ~ axc11n .
      Normally, ~ axc11 should be used rather than ~ ax-c11 , except by theorems
-     specifically studying the latter's properties.  (Contributed by NM,
-     16-May-2008.)  (Proof shortened by Wolf Lammen, 21-Apr-2018.)
-     (New usage is discouraged.) $)
+     specifically studying the latter's properties.  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  Use the weaker ~ axc11v when
+     possible.  (Contributed by NM, 16-May-2008.)  (Proof shortened by Wolf
+     Lammen, 21-Apr-2018.)  (New usage is discouraged.) $)
   axc11 $p |- ( A. x x = y -> ( A. x ph -> A. y ph ) ) $=
     ( wal wi axc11r aecoms ) ABDACDECBABCFG $.
 
   $( All variables are effectively bound in an identical variable specifier.
-     (Contributed by NM, 13-May-1993.)  (Proof shortened by Wolf Lammen,
-     21-Apr-2018.)  (New usage is discouraged.) $)
+     Usage of this theorem is discouraged because it depends on ~ ax-13 .  Use
+     the weaker ~ hbaev when possible.  (Contributed by NM, 13-May-1993.)
+     (Proof shortened by Wolf Lammen, 21-Apr-2018.)
+     (New usage is discouraged.) $)
   hbae $p |- ( A. x x = y -> A. z A. x x = y ) $=
     ( weq wal wi wn sp axc9 syl7 axc11r axc11 pm2.43i syl5 pm2.61ii axc4i ax-11
     syl ) ABDZAEZSCEZAETCESUAACADCEZCBDCEZTUAFTSUBGUCGUASAHABCIJSACKTSBEZUCUATU
     DSABLMSBCKNOPSACQR $.
 
-  $( All variables are effectively bound in a distinct variable specifier.  A
-     version with a distinct variable condition based on fewer axioms is
-     ~ hbnaev .  Lemma L19 in [Megill] p. 446 (p. 14 of the preprint).
-     (Contributed by NM, 13-May-1993.)  (New usage is discouraged.) $)
+  $( All variables are effectively bound in a distinct variable specifier.
+     Lemma L19 in [Megill] p. 446 (p. 14 of the preprint).  Usage of this
+     theorem is discouraged because it depends on ~ ax-13 .  Use the weaker
+     ~ hbnaev when possible.  (Contributed by NM, 13-May-1993.)
+     (New usage is discouraged.) $)
   hbnae $p |- ( -. A. x x = y -> A. z -. A. x x = y ) $=
     ( weq wal hbae hbn ) ABDAECABCFG $.
 
   $( All variables are effectively bound in an identical variable specifier.
+     Usage of this theorem is discouraged because it depends on ~ ax-13 .
      (Contributed by Mario Carneiro, 11-Aug-2016.)
      (New usage is discouraged.) $)
   nfae $p |- F/ z A. x x = y $=
     ( weq wal hbae nf5i ) ABDAECABCFG $.
 
   $( All variables are effectively bound in a distinct variable specifier.  See
-     also ~ nfnaew .  (Contributed by Mario Carneiro, 11-Aug-2016.)
-     (New usage is discouraged.) $)
+     also ~ nfnaew .  Usage of this theorem is discouraged because it depends
+     on ~ ax-13 .  Use the weaker ~ nfnaew when possible.  (Contributed by
+     Mario Carneiro, 11-Aug-2016.)  (New usage is discouraged.) $)
   nfnae $p |- F/ z -. A. x x = y $=
     ( weq wal nfae nfn ) ABDAECABCFG $.
 
   ${
     hbnaes.1 $e |- ( A. z -. A. x x = y -> ph ) $.
-    $( Rule that applies ~ hbnae to antecedent.  (Contributed by NM,
+    $( Rule that applies ~ hbnae to antecedent.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  (Contributed by NM,
        15-May-1993.)  (New usage is discouraged.) $)
     hbnaes $p |- ( -. A. x x = y -> ph ) $=
       ( weq wal wn hbnae syl ) BCFBGHZKDGABCDIEJ $.
@@ -21298,9 +21365,9 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     $d x y z $.  $d z ph $.
     axc16i.1 $e |- ( x = z -> ( ph <-> ps ) ) $.
     axc16i.2 $e |- ( ps -> A. x ps ) $.
-    $( Inference with ~ axc16 as its conclusion.  (Contributed by NM,
-       20-May-2008.)  (Proof modification is discouraged.)
-       (New usage is discouraged.) $)
+    $( Inference with ~ axc16 as its conclusion.  Usage of ~ axc16 is preferred
+       since it requires fewer axioms.  (Contributed by NM, 20-May-2008.)
+       (Proof modification is discouraged.)  (New usage is discouraged.) $)
     axc16i $p |- ( A. x x = y -> ( ph -> A. x ph ) ) $=
       ( weq wal wi nfv ax7 cbv3 spimvw equcomi syl syl5com alimdv mpcom alimi
       biimpcd nf5i biimprd syl6com 3syl ) CDHZCIEDHZEIZCEHZEIZAACIZJUFUGCEUFEKU
@@ -21320,16 +21387,20 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   ${
     dral1.1 $e |- ( A. x x = y -> ( ph <-> ps ) ) $.
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
-       Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).
-       (Contributed by NM, 27-Feb-2005.)  Allow a shortening of ~ dral1 .
-       (Revised by Wolf Lammen, 4-Mar-2018.)  (New usage is discouraged.) $)
+       Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .  Usage of
+       ~ albidv is preferred, which requires fewer axioms.  (Contributed by NM,
+       27-Feb-2005.)  Allow a shortening of ~ dral1 .  (Revised by Wolf Lammen,
+       4-Mar-2018.)  (New usage is discouraged.) $)
     dral2 $p |- ( A. x x = y -> ( A. z ph <-> A. z ps ) ) $=
       ( weq wal nfae albid ) CDGCHABECDEIFJ $.
 
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
-       Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).
-       (Contributed by NM, 24-Nov-1994.)  Remove dependency on ~ ax-11 .
-       (Revised by Wolf Lammen, 6-Sep-2018.)  (New usage is discouraged.) $)
+       Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ dral1v if possible.  (Contributed by NM, 24-Nov-1994.)  Remove
+       dependency on ~ ax-11 .  (Revised by Wolf Lammen, 6-Sep-2018.)
+       (New usage is discouraged.) $)
     dral1 $p |- ( A. x x = y -> ( A. x ph <-> A. y ps ) ) $=
       ( weq wal nfa1 albid axc11 axc11r impbid bitrd ) CDFZCGZACGBCGZBDGZOABCNC
       HEIOPQBCDJBDCKLM $.
@@ -21343,26 +21414,33 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
       DIBDCJKL $.
 
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
-       Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).
-       (Contributed by NM, 27-Feb-2005.)  (New usage is discouraged.) $)
+       Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ drex1v if possible.  (Contributed by NM, 27-Feb-2005.)
+       (New usage is discouraged.) $)
     drex1 $p |- ( A. x x = y -> ( E. x ph <-> E. y ps ) ) $=
       ( weq wal wn wex notbid dral1 df-ex 3bitr4g ) CDFCGZAHZCGZHBHZDGZHACIBDIN
       PROQCDNABEJKJACLBDLM $.
 
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
-       Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).
-       (Contributed by NM, 27-Feb-2005.)  (New usage is discouraged.) $)
+       Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .  Usage of
+       ~ exbidv is preferred, which requires fewer axioms.  (Contributed by NM,
+       27-Feb-2005.)  (New usage is discouraged.) $)
     drex2 $p |- ( A. x x = y -> ( E. z ph <-> E. z ps ) ) $=
       ( weq wal nfae exbid ) CDGCHABECDEIFJ $.
 
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
-       (Contributed by Mario Carneiro, 4-Oct-2016.)
-       (New usage is discouraged.) $)
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       Use the weaker ~ drnf1v if possible.  (Contributed by Mario Carneiro,
+       4-Oct-2016.)  (New usage is discouraged.) $)
     drnf1 $p |- ( A. x x = y -> ( F/ x ph <-> F/ y ps ) ) $=
       ( weq wal wi wnf dral1 imbi12d nf5 3bitr4g ) CDFCGZAACGZHZCGBBDGZHZDGACIB
       DIPRCDNABOQEABCDEJKJACLBDLM $.
 
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       Usage of ~ nfbidv is preferred, which requires fewer axioms.
        (Contributed by Mario Carneiro, 4-Oct-2016.)  (Proof shortened by Wolf
        Lammen, 5-May-2018.)  (New usage is discouraged.) $)
     drnf2 $p |- ( A. x x = y -> ( F/ z ph <-> F/ z ps ) ) $=
@@ -21373,15 +21451,19 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     nfald2.1 $e |- F/ y ph $.
     nfald2.2 $e |- ( ( ph /\ -. A. x x = y ) -> F/ x ps ) $.
     $( Variation on ~ nfald which adds the hypothesis that ` x ` and ` y ` are
-       distinct in the inner subproof.  (Contributed by Mario Carneiro,
-       8-Oct-2016.)  (New usage is discouraged.) $)
+       distinct in the inner subproof.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Check out ~ nfald for a version
+       requiring fewer axioms.  (Contributed by Mario Carneiro, 8-Oct-2016.)
+       (New usage is discouraged.) $)
     nfald2 $p |- ( ph -> F/ x A. y ps ) $=
       ( weq wal wnf wn wa nfnae nfan nfald ex nfa1 biidd drnf1 mpbiri pm2.61d2
       ) ACDGCHZBDHZCIZAUAJZUCAUDKBCDAUDDECDDLMFNOUAUCUBDIBDPUBUBCDUAUBQRST $.
 
     $( Variation on ~ nfexd which adds the hypothesis that ` x ` and ` y ` are
-       distinct in the inner subproof.  (Contributed by Mario Carneiro,
-       8-Oct-2016.)  (New usage is discouraged.) $)
+       distinct in the inner subproof.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Check out ~ nfexd for a version
+       requiring fewer axioms.  (Contributed by Mario Carneiro, 8-Oct-2016.)
+       (New usage is discouraged.) $)
     nfexd2 $p |- ( ph -> F/ x E. y ps ) $=
       ( wex wn wal df-ex weq wa nfnd nfald2 nfxfrd ) BDGBHZDIZHACBDJAQCAPCDEACD
       KCIHLBCFMNMO $.
@@ -21392,8 +21474,10 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     $( Distribution of existential quantifiers, with a bound-variable
        hypothesis saying that ` y ` is not free in ` ph ` , but ` x ` can be
        free in ` ph ` (and there is no distinct variable condition on ` x ` and
-       ` y ` ).  (Contributed by Mario Carneiro, 20-Mar-2013.)  (Proof
-       shortened by Wolf Lammen, 14-May-2018.)  (New usage is discouraged.) $)
+       ` y ` ).  Usage of this theorem is discouraged because it depends on
+       ~ ax-13 .  Check out ~ exdistr for a version requiring fewer axioms.
+       (Contributed by Mario Carneiro, 20-Mar-2013.)  (Proof shortened by Wolf
+       Lammen, 14-May-2018.)  (New usage is discouraged.) $)
     exdistrf $p |- ( E. x E. y ( ph /\ ps ) -> E. x ( ph /\ E. y ps ) ) $=
       ( wa wex weq wal wi 19.8a anim2i eximi biidd drex1 syl5ibr wn 19.40 19.9d
       nfe1 anim1d syl56 pm2.61i exlimi ) ABFZDGZABDGZFZCGZCUHCTCDHCIZUFUIJUFUIU
@@ -21405,7 +21489,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     dvelimf.1 $e |- F/ x ph $.
     dvelimf.2 $e |- F/ z ps $.
     dvelimf.3 $e |- ( z = y -> ( ph <-> ps ) ) $.
-    $( Version of ~ dvelimv without any variable restrictions.  (Contributed by
+    $( Version of ~ dvelimv without any variable restrictions.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
        NM, 1-Oct-2002.)  (Revised by Mario Carneiro, 6-Oct-2016.)  (Proof
        shortened by Wolf Lammen, 11-May-2018.)  (New usage is discouraged.) $)
     dvelimf $p |- ( -. A. x x = y -> F/ x ps ) $=
@@ -21420,7 +21505,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     dvelimdf.3 $e |- ( ph -> F/ x ps ) $.
     dvelimdf.4 $e |- ( ph -> F/ z ch ) $.
     dvelimdf.5 $e |- ( ph -> ( z = y -> ( ps <-> ch ) ) ) $.
-    $( Deduction form of ~ dvelimf .  (Contributed by NM, 7-Apr-2004.)
+    $( Deduction form of ~ dvelimf .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by NM, 7-Apr-2004.)
        (Revised by Mario Carneiro, 6-Oct-2016.)  (Proof shortened by Wolf
        Lammen, 11-May-2018.)  (New usage is discouraged.) $)
     dvelimdf $p |- ( ph -> ( -. A. x x = y -> F/ x ch ) ) $=
@@ -21432,8 +21518,10 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     dvelimh.1 $e |- ( ph -> A. x ph ) $.
     dvelimh.2 $e |- ( ps -> A. z ps ) $.
     dvelimh.3 $e |- ( z = y -> ( ph <-> ps ) ) $.
-    $( Version of ~ dvelim without any variable restrictions.  (Contributed by
-       NM, 1-Oct-2002.)  (Proof shortened by Wolf Lammen, 11-May-2018.)
+    $( Version of ~ dvelim without any variable restrictions.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  Check out
+       ~ dvelimhw for a version requiring fewer axioms.  (Contributed by NM,
+       1-Oct-2002.)  (Proof shortened by Wolf Lammen, 11-May-2018.)
        (New usage is discouraged.) $)
     dvelimh $p |- ( -. A. x x = y -> ( ps -> A. x ps ) ) $=
       ( weq wal wn nf5i dvelimf nf5rd ) CDICJKBCABCDEACFLBEGLHMN $.
@@ -21455,8 +21543,10 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
        with ` A. x A. z ` , conjoin them, and apply ~ dvelimdf .
 
        Other variants of this theorem are ~ dvelimh (with no distinct variable
-       restrictions) and ~ dvelimhw (that avoids ~ ax-13 ).  (Contributed by
-       NM, 23-Nov-1994.)  (New usage is discouraged.) $)
+       restrictions) and ~ dvelimhw (that avoids ~ ax-13 ).  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  Check out
+       ~ dvelimhw for a version requiring fewer axioms.  (Contributed by NM,
+       23-Nov-1994.)  (New usage is discouraged.) $)
     dvelim $p |- ( -. A. x x = y -> ( ps -> A. x ps ) ) $=
       ( ax-5 dvelimh ) ABCDEFBEHGI $.
   $}
@@ -21465,8 +21555,10 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     $d x ph $.  $d z ps $.
     dvelimv.1 $e |- ( z = y -> ( ph <-> ps ) ) $.
     $( Similar to ~ dvelim with first hypothesis replaced by a distinct
-       variable condition.  (Contributed by NM, 25-Jul-2015.)  (Proof shortened
-       by Wolf Lammen, 30-Apr-2018.)  (New usage is discouraged.) $)
+       variable condition.  Usage of this theorem is discouraged because it
+       depends on ~ ax-13 .  Check out ~ dvelimhw for a version requiring fewer
+       axioms.  (Contributed by NM, 25-Jul-2015.)  (Proof shortened by Wolf
+       Lammen, 30-Apr-2018.)  (New usage is discouraged.) $)
     dvelimv $p |- ( -. A. x x = y -> ( ps -> A. x ps ) ) $=
       ( ax-5 dvelim ) ABCDEACGFH $.
   $}
@@ -21475,7 +21567,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     $d z ps $.
     dvelimnf.1 $e |- F/ x ph $.
     dvelimnf.2 $e |- ( z = y -> ( ph <-> ps ) ) $.
-    $( Version of ~ dvelim using "not free" notation.  (Contributed by Mario
+    $( Version of ~ dvelim using "not free" notation.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  (Contributed by Mario
        Carneiro, 9-Oct-2016.)  (New usage is discouraged.) $)
     dvelimnf $p |- ( -. A. x x = y -> F/ x ps ) $=
       ( nfv dvelimf ) ABCDEFBEHGI $.
@@ -21491,7 +21584,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   $}
 
   $( A variable introduction law for equality.  Lemma 15 of [Monk2] p. 109,
-     however we do not require ` z ` to be distinct from ` x ` and ` y ` .  See
+     however we do not require ` z ` to be distinct from ` x ` and ` y ` .
+     Usage of this theorem is discouraged because it depends on ~ ax-13 .  See
      ~ equvinv for a shorter proof requiring fewer axioms when ` z ` is
      required to be distinct from ` x ` and ` y ` .  (Contributed by NM,
      10-Jan-1993.)  (Proof shortened by Andrew Salmon, 25-May-2011.)  (Proof
@@ -21511,9 +21605,11 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     ECLMUANUBUBCRUFCABOUBUECUDUBUEGCCBSUGPQMT $.
 
   $( A variable elimination law for equality with no distinct variable
-     requirements.  Compare ~ equvini .  (Contributed by NM, 1-Mar-2013.)
-     (Proof shortened by Mario Carneiro, 17-Oct-2016.)  (Proof shortened by
-     Wolf Lammen, 15-Jun-2019.)  (New usage is discouraged.) $)
+     requirements.  Compare ~ equvini .  Usage of this theorem is discouraged
+     because it depends on ~ ax-13 .  Use the weaker ~ equvelv when possible.
+     (Contributed by NM, 1-Mar-2013.)  (Proof shortened by Mario Carneiro,
+     17-Oct-2016.)  (Proof shortened by Wolf Lammen, 15-Jun-2019.)
+     (New usage is discouraged.) $)
   equvel $p |- ( A. z ( z = x <-> z = y ) -> x = y ) $=
     ( weq wb wal wex albi wi ax6e biimpr ax7 syli com12 eximii 19.35i spsd a1dd
     sps wn wa nfeqf 19.9d ex bija sylc ) CADZCBDZEZCFUGCFZUHCFZEABDZCGZULUGUHCH
@@ -21521,7 +21617,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     LCUNQSRUJTZUKTZUOULUPUQUACABCUBUCUDUEUF $.
 
   $( A property related to substitution that unlike ~ equs5 does not require a
-     distinctor antecedent.  See ~ equs5av and ~ equs5aALT for proofs using
+     distinctor antecedent.  Usage of this theorem is discouraged because it
+     depends on ~ ax-13 .  See ~ equs5av and ~ equs5aALT for proofs using
      ~ ax-12 but not ~ ax13 .  (Contributed by NM, 2-Feb-2007.)
      (New usage is discouraged.) $)
   equs5a $p |- ( E. x ( x = y /\ A. y ph ) -> A. x ( x = y -> ph ) ) $=
@@ -21529,8 +21626,9 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
   $( A property related to substitution that unlike ~ equs5 does not require a
      distinctor antecedent.  See ~ equs5eALT for an alternate proof using
-     ~ ax-12 but not ~ ax13 .  (Contributed by NM, 2-Feb-2007.)  (Proof
-     shortened by Wolf Lammen, 15-Jan-2018.)  (New usage is discouraged.) $)
+     ~ ax-12 but not ~ ax13 .  Usage of this theorem is discouraged because it
+     depends on ~ ax-13 .  (Contributed by NM, 2-Feb-2007.)  (Proof shortened
+     by Wolf Lammen, 15-Jan-2018.)  (New usage is discouraged.) $)
   equs5e $p |- ( E. x ( x = y /\ ph ) -> A. x ( x = y -> E. y ph ) ) $=
     ( weq wa wex wi wal nfa1 ax12 hbe1 19.23bi impel exlimi ) BCDZAEOACFZGZBHZB
     QBIOPCHZRAPBCJASCACKLMN $.
@@ -21541,7 +21639,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
        The implication "to the left" is ~ equs4 and does not require the
        non-freeness hypothesis.  Theorem ~ sb56 replaces the non-freeness
        hypothesis with a disjoint variable condition and ~ equs5 replaces it
-       with a distinctor as antecedent.  (Contributed by NM, 25-Apr-2008.)
+       with a distinctor as antecedent.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by NM, 25-Apr-2008.)
        (Revised by Mario Carneiro, 4-Oct-2016.)  (New usage is discouraged.) $)
     equs45f $p |- ( E. x ( x = y /\ ph ) <-> A. x ( x = y -> ph ) ) $=
       ( weq wa wex wi wal nf5ri anim2i eximi equs5a syl equs4 impbii ) BCEZAFZB
@@ -21550,7 +21649,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
   $( Lemma used in proofs of substitution properties.  If there is a disjoint
      variable condition on ` x , y ` , then ~ sb56 can be used instead; if
-     ` y ` is not free in ` ph ` , then ~ equs45f can be used.  (Contributed by
+     ` y ` is not free in ` ph ` , then ~ equs45f can be used.  Usage of this
+     theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
      NM, 14-May-1993.)  (Revised by BJ, 1-Oct-2018.)
      (New usage is discouraged.) $)
   equs5 $p |- ( -. A. x x = y ->
@@ -21560,12 +21660,14 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
   ${
     $d w z x $.  $d w y $.
-    $( Quantifier introduction when one pair of variables is distinct.
+    $( Quantifier introduction when one pair of variables is distinct.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 2-Jan-2002.)  (New usage is discouraged.) $)
     dveel1 $p |- ( -. A. x x = y -> ( y e. z -> A. x y e. z ) ) $=
       ( vw wel elequ1 dvelimv ) DCEBCEABDDBCFG $.
 
-    $( Quantifier introduction when one pair of variables is distinct.
+    $( Quantifier introduction when one pair of variables is distinct.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 2-Jan-2002.)  (New usage is discouraged.) $)
     dveel2 $p |- ( -. A. x x = y -> ( z e. y -> A. x z e. y ) ) $=
       ( vw wel elequ2 dvelimv ) CDECBEABDDBCFG $.
@@ -21579,7 +21681,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
        Note that ` w ` is a dummy variable introduced in the proof.  Its
        purpose is to satisfy the distinct variable requirements of ~ dveel2 and
        ~ ax-5 .  By the end of the proof it has vanished, and the final theorem
-       has no distinct variable requirements.  (Contributed by NM,
+       has no distinct variable requirements.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  (Contributed by NM,
        29-Jun-1995.)  (Proof modification is discouraged.)
        (New usage is discouraged.) $)
     axc14 $p |- ( -. A. z z = x -> ( -. A. z z = y ->
@@ -21591,36 +21694,43 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
   ${
     sb6x.1 $e |- F/ x ph $.
-    $( Equivalence involving substitution for a variable not free.
-       (Contributed by NM, 2-Jun-1993.)  (Revised by Mario Carneiro,
-       4-Oct-2016.)  (New usage is discouraged.) $)
+    $( Equivalence involving substitution for a variable not free.  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .  Usage of
+       ~ sb6 is preferred, which requires fewer axioms.  (Contributed by NM,
+       2-Jun-1993.)  (Revised by Mario Carneiro, 4-Oct-2016.)
+       (New usage is discouraged.) $)
     sb6x $p |- ( [ y / x ] ph <-> A. x ( x = y -> ph ) ) $=
       ( wsb weq wi wal sbf biidd equsal bitr4i ) ABCEABCFZAGBHABCDIAABCDMAJKL
       $.
   $}
 
-  $( Substitution does not change an identical variable specifier.
-     (Contributed by NM, 15-May-1993.)  (New usage is discouraged.) $)
+  $( Substitution does not change an identical variable specifier.  Usage of
+     this theorem is discouraged because it depends on ~ ax-13 .  (Contributed
+     by NM, 15-May-1993.)  (New usage is discouraged.) $)
   sbequ5 $p |- ( [ w / z ] A. x x = y <-> A. x x = y ) $=
     ( weq wal nfae sbf ) ABEAFCDABCGH $.
 
-  $( Substitution does not change a distinctor.  (Contributed by NM,
+  $( Substitution does not change a distinctor.  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  (Contributed by NM,
      5-Aug-1993.)  (New usage is discouraged.) $)
   sbequ6 $p |- ( [ w / z ] -. A. x x = y <-> -. A. x x = y ) $=
     ( weq wal wn nfnae sbf ) ABEAFGCDABCHI $.
 
   ${
     sb5rf.1 $e |- F/ y ph $.
-    $( Reversed substitution.  (Contributed by NM, 3-Feb-2005.)  (Revised by
+    $( Reversed substitution.  Usage of this theorem is discouraged because it
+       depends on ~ ax-13 .  (Contributed by NM, 3-Feb-2005.)  (Revised by
        Mario Carneiro, 6-Oct-2016.)  (Proof shortened by Wolf Lammen,
        20-Sep-2018.)  (New usage is discouraged.) $)
     sb5rf $p |- ( ph <-> E. y ( y = x /\ [ y / x ] ph ) ) $=
       ( weq wsb wa wex sbequ12r equsex bicomi ) CBEABCFZGCHALACBDACBIJK $.
 
     $( Reversed substitution.  For a version requiring disjoint variables, but
-       fewer axioms, see ~ sb6rfv .  (Contributed by NM, 1-Aug-1993.)  (Revised
-       by Mario Carneiro, 6-Oct-2016.)  (Proof shortened by Wolf Lammen,
-       21-Sep-2018.)  (New usage is discouraged.) $)
+       fewer axioms, see ~ sb6rfv .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ sb6rfv if possible.
+       (Contributed by NM, 1-Aug-1993.)  (Revised by Mario Carneiro,
+       6-Oct-2016.)  (Proof shortened by Wolf Lammen, 21-Sep-2018.)
+       (New usage is discouraged.) $)
     sb6rf $p |- ( ph <-> A. y ( y = x -> [ y / x ] ph ) ) $=
       ( weq wsb wi wal sbequ12r equsal bicomi ) CBEABCFZGCHALACBDACBIJK $.
   $}
@@ -21639,7 +21749,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
      represented by distinct variables.  This theorem merges two ~ ax6e
      instances ` E. z z = x ` and ` E. w w = y ` into a common expression.
      Alan Sare contributed a variant of this theorem with distinct variable
-     conditions before, see ~ ax6e2nd .  (Contributed by Wolf Lammen,
+     conditions before, see ~ ax6e2nd .  Usage of this theorem is discouraged
+     because it depends on ~ ax-13 .  (Contributed by Wolf Lammen,
      27-Sep-2018.)  (New usage is discouraged.) $)
   2ax6elem $p |- ( -. A. w w = z -> E. z E. w ( z = x /\ w = y ) ) $=
     ( weq wal wn wex ax6e nfnae nfan nfeqf pm3.21 spimed eximd mpi nfae equvini
@@ -21651,7 +21762,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     $d w z $.
     $( We can always find values matching ` x ` and ` y ` , as long as they are
        represented by distinct variables.  Version of ~ 2ax6elem with a
-       distinct variable constraint.  (Contributed by Wolf Lammen,
+       distinct variable constraint.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by Wolf Lammen,
        28-Sep-2018.)  (Proof shortened by Wolf Lammen, 3-Oct-2023.)
        (New usage is discouraged.) $)
     2ax6e $p |- E. z E. w ( z = x /\ w = y ) $=
@@ -21670,7 +21782,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     $d w z $.
     2sb5rf.1 $e |- F/ z ph $.
     2sb5rf.2 $e |- F/ w ph $.
-    $( Reversed double substitution.  (Contributed by NM, 3-Feb-2005.)
+    $( Reversed double substitution.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by NM, 3-Feb-2005.)
        (Revised by Mario Carneiro, 6-Oct-2016.)  Remove distinct variable
        constraints.  (Revised by Wolf Lammen, 28-Sep-2018.)
        (New usage is discouraged.) $)
@@ -21680,7 +21793,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
       wsb pm5.32i bitr4i ) ADBHZECHZIZAIZEJZDJZUDACESZBDSZIZEJDJUDEJZAIZDJUKDJZ
       AIUGAUKADFKUFULDUDAEGKLUMABCDEMNOUJUEDEUDUIAUBUIUHUCAUHDBPAECPQTRUA $.
 
-    $( Reversed double substitution.  (Contributed by NM, 3-Feb-2005.)
+    $( Reversed double substitution.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by NM, 3-Feb-2005.)
        (Revised by Mario Carneiro, 6-Oct-2016.)  Remove variable constraints.
        (Revised by Wolf Lammen, 28-Sep-2018.)  (Proof shortened by Wolf Lammen,
        13-Apr-2023.)  (New usage is discouraged.) $)
@@ -21705,8 +21819,9 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
   ${
     $d x y ph $.
-    $( Elimination of double substitution.  (Contributed by NM, 5-Aug-1993.)
-       (Proof shortened by Wolf Lammen, 29-Sep-2018.)
+    $( Elimination of double substitution.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  (Contributed by NM,
+       5-Aug-1993.)  (Proof shortened by Wolf Lammen, 29-Sep-2018.)
        (New usage is discouraged.) $)
     sbel2x $p |- ( ph <-> E. x E. y ( ( x = z /\ y = w ) /\
                      [ y / w ] [ x / z ] ph ) ) $=
@@ -21717,8 +21832,9 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   ${
     $d y x $.  $d y t $.  $d y ph $.
     $( Simplified definition of substitution when variables are distinct.
-       Version of ~ sb6 with a distinctor.  (Contributed by NM, 27-May-1997.)
-       Revise ~ df-sb .  (Revised by Wolf Lammen, 21-Feb-2024.)
+       Version of ~ sb6 with a distinctor.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  (Contributed by NM,
+       27-May-1997.)  Revise ~ df-sb .  (Revised by Wolf Lammen, 21-Feb-2024.)
        (New usage is discouraged.) $)
     sb4b $p |- ( -. A. x x = t -> ( [ t / x ] ph
                                               <-> A. x ( x = t -> ph ) ) ) $=
@@ -21740,7 +21856,8 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
   $}
 
   $( Simplified definition of substitution when variables are distinct.  This
-     is the biconditional strengthening of ~ sb3 .  (Contributed by BJ,
+     is the biconditional strengthening of ~ sb3 .  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  (Contributed by BJ,
      6-Oct-2018.)  Shorten ~ sb3 .  (Revised by Wolf Lammen, 21-Feb-2021.)
      (New usage is discouraged.) $)
   sb3b $p |- ( -. A. x x = y -> ( [ y / x ] ph <-> E. x ( x = y /\ ph ) ) ) $=
@@ -21748,25 +21865,27 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
     LM $.
 
   $( One direction of a simplified definition of substitution when variables
-     are distinct.  (Contributed by NM, 5-Aug-1993.)  (Proof shortened by Wolf
+     are distinct.  Usage of this theorem is discouraged because it depends on
+     ~ ax-13 .  (Contributed by NM, 5-Aug-1993.)  (Proof shortened by Wolf
      Lammen, 21-Feb-2024.)  (New usage is discouraged.) $)
   sb3 $p |- ( -. A. x x = y -> ( E. x ( x = y /\ ph ) -> [ y / x ] ph ) ) $=
     ( weq wal wn wsb wa wex sb3b biimprd ) BCDZBEFABCGLAHBIABCJK $.
 
   $( One direction of a simplified definition of substitution.  The converse
      requires either a disjoint variable condition ( ~ sb5 ) or a non-freeness
-     hypothesis ( ~ sb5f ).  See also ~ sb1v .  (Contributed by NM,
-     13-May-1993.)  Revise ~ df-sb .  (Revised by Wolf Lammen, 21-Feb-2024.)
-     (New usage is discouraged.) $)
+     hypothesis ( ~ sb5f ).  Usage of this theorem is discouraged because it
+     depends on ~ ax-13 .  Use the weaker ~ sb1v when possible.  (Contributed
+     by NM, 13-May-1993.)  Revise ~ df-sb .  (Revised by Wolf Lammen,
+     21-Feb-2024.)  (New usage is discouraged.) $)
   sb1 $p |- ( [ y / x ] ph -> E. x ( x = y /\ ph ) ) $=
     ( weq wal wsb wa wex wi spsbe pm3.2 aleximi syl5 wn sb3b biimpd pm2.61i ) B
     CDZBEZABCFZRAGZBHZITABHSUBABCJRAUABRAKLMSNTUBABCOPQ $.
 
   $( One direction of a simplified definition of substitution.  The converse
      requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
-     hypothesis ( ~ sb6f ).  (Contributed by NM, 13-May-1993.)  Revise
-     ~ df-sb .  (Revised by Wolf Lammen, 26-Jul-2023.)
-     (New usage is discouraged.) $)
+     hypothesis ( ~ sb6f ).  Usage of this theorem is discouraged because it
+     depends on ~ ax-13 .  (Contributed by NM, 13-May-1993.)  Revise ~ df-sb .
+     (Revised by Wolf Lammen, 26-Jul-2023.)  (New usage is discouraged.) $)
   sb2 $p |- ( A. x ( x = y -> ph ) -> [ y / x ] ph ) $=
     ( weq wal wi wsb pm2.27 al2imi stdpc4 syl6 wn sb4b biimprd pm2.61i ) BCDZBE
     ZPAFZBEZABCGZFQSABETPRABPAHIABCJKQLTSABCMNO $.
@@ -21802,8 +21921,10 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
     ( weq wal wn wsb wa wex sb1 sb3 impbid2 ) BCDZBEFABCGMAHBIABCJABCKL $.
 
   $( A version of one implication of ~ sb4b that does not require a distinctor
-     antecedent.  (Contributed by NM, 2-Feb-2007.)  Revise ~ df-sb .  (Revised
-     by Wolf Lammen, 28-Jul-2023.)  (New usage is discouraged.) $)
+     antecedent.  Usage of this theorem is discouraged because it depends on
+     ~ ax-13 .  Use the weaker ~ sb4av when possible.  (Contributed by NM,
+     2-Feb-2007.)  Revise ~ df-sb .  (Revised by Wolf Lammen, 28-Jul-2023.)
+     (New usage is discouraged.) $)
   sb4a $p |- ( [ t / x ] A. t ph -> A. x ( x = t -> ph ) ) $=
     ( weq wal wsb wi sbequ2 sps axc11r ala1 syl6 syld wn sp imim2i alimi syl6bi
     sb4b pm2.61i ) BCDZBEZACEZBCFZUAAGZBEZGUBUDUCUFUAUDUCGBUCBCHIUBUCABEUFACBJA
@@ -21813,6 +21934,7 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
      15 of the preprint).  This was the original definition before ~ df-sb .
      Note that it does not require dummy variables in its definiens; this is
      done by having ` x ` free in the first conjunct and bound in the second.
+     Usage of this theorem is discouraged because it depends on ~ ax-13 .
      (Contributed by BJ, 9-Jul-2023.)  Revise ~ df-sb .  (Revised by Wolf
      Lammen, 29-Jul-2023.)  (New usage is discouraged.) $)
   dfsb1 $p |- ( [ y / x ] ph <->
@@ -21918,29 +22040,34 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
     ( weq wsb wa wi wex pm3.4 19.8a dfsb1 sylanbrc ex ) BCDZAABCEZNAFZNAGPBHONA
     IPBJABCKLM $.
 
-  $( Bound-variable hypothesis builder for substitution.  (Contributed by NM,
+  $( Bound-variable hypothesis builder for substitution.  Usage of this theorem
+     is discouraged because it depends on ~ ax-13 .  (Contributed by NM,
      14-May-1993.)  (New usage is discouraged.) $)
   hbsb2 $p |- ( -. A. x x = y -> ( [ y / x ] ph -> A. x [ y / x ] ph ) ) $=
     ( weq wal wn wsb wi sb4b sb2 axc4i syl6bi ) BCDZBEFABCGZMAHZBENBEABCIONBABC
     JKL $.
 
-  $( Bound-variable hypothesis builder for substitution.  (Contributed by Mario
+  $( Bound-variable hypothesis builder for substitution.  Usage of this theorem
+     is discouraged because it depends on ~ ax-13 .  (Contributed by Mario
      Carneiro, 4-Oct-2016.)  (New usage is discouraged.) $)
   nfsb2 $p |- ( -. A. x x = y -> F/ x [ y / x ] ph ) $=
     ( weq wal wn wsb nfna1 hbsb2 nf5d ) BCDZBEFABCGBKBHABCIJ $.
 
   $( Special case of a bound-variable hypothesis builder for substitution.
+     Usage of this theorem is discouraged because it depends on ~ ax-13 .
      (Contributed by NM, 2-Feb-2007.)  (New usage is discouraged.) $)
   hbsb2a $p |- ( [ y / x ] A. y ph -> A. x [ y / x ] ph ) $=
     ( wal wsb weq wi sb4a sb2 axc4i syl ) ACDBCEBCFAGZBDABCEZBDABCHLMBABCIJK $.
 
   $( One direction of a simplified definition of substitution that unlike
-     ~ sb4b does not require a distinctor antecedent.  (Contributed by NM,
+     ~ sb4b does not require a distinctor antecedent.  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  (Contributed by NM,
      2-Feb-2007.)  (New usage is discouraged.) $)
   sb4e $p |- ( [ y / x ] ph -> A. x ( x = y -> E. y ph ) ) $=
     ( wsb weq wa wex wi wal sb1 equs5e syl ) ABCDBCEZAFBGMACGHBIABCJABCKL $.
 
   $( Special case of a bound-variable hypothesis builder for substitution.
+     Usage of this theorem is discouraged because it depends on ~ ax-13 .
      (Contributed by NM, 2-Feb-2007.)  (New usage is discouraged.) $)
   hbsb2e $p |- ( [ y / x ] ph -> A. x [ y / x ] E. y ph ) $=
     ( wsb weq wex wi wal sb4e sb2 axc4i syl ) ABCDBCEACFZGZBHMBCDZBHABCINOBMBCJ
@@ -21949,6 +22076,8 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
   ${
     hbsb3.1 $e |- ( ph -> A. y ph ) $.
     $( If ` y ` is not free in ` ph ` , ` x ` is not free in ` [ y / x ] ph ` .
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       Check out ~ bj-hbsb3v for a weaker version requiring less axioms.
        (Contributed by NM, 14-May-1993.)  (New usage is discouraged.) $)
     hbsb3 $p |- ( [ y / x ] ph -> A. x [ y / x ] ph ) $=
       ( wsb wal sbimi hbsb2a syl ) ABCEZACFZBCEJBFAKBCDGABCHI $.
@@ -21957,8 +22086,9 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
   ${
     nfs1.1 $e |- F/ y ph $.
     $( If ` y ` is not free in ` ph ` , ` x ` is not free in ` [ y / x ] ph ` .
-       (Contributed by Mario Carneiro, 11-Aug-2016.)
-       (New usage is discouraged.) $)
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       Check out ~ nfs1v for a version requiring less axioms.  (Contributed by
+       Mario Carneiro, 11-Aug-2016.)  (New usage is discouraged.) $)
     nfs1 $p |- F/ x [ y / x ] ph $=
       ( wsb nf5ri hbsb3 nf5i ) ABCEBABCACDFGH $.
   $}
@@ -21984,18 +22114,23 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
       BCDBDGABCHMONAADBMAIJKL $.
   $}
 
-  $( Substitution applied to an atomic wff.  (Contributed by NM, 10-May-1993.)
+  $( Substitution applied to an atomic wff.  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  Use the weaker ~ equsb1v if
+     possible.  (Contributed by NM, 10-May-1993.)
      (New usage is discouraged.) $)
   equsb1 $p |- [ y / x ] x = y $=
     ( weq wi wsb sb2 id mpg ) ABCZIDIABEAIABFIGH $.
 
-  $( Substitution applied to an atomic wff.  (Contributed by NM, 10-May-1993.)
+  $( Substitution applied to an atomic wff.  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  Check out ~ equsb1v for a
+     version requiring less axioms.  (Contributed by NM, 10-May-1993.)
      (New usage is discouraged.) $)
   equsb2 $p |- [ y / x ] y = x $=
     ( weq wi wsb sb2 equcomi mpg ) ABCBACZDIABEAIABFABGH $.
 
   $( An alternate definition of proper substitution that, like ~ dfsb1 , mixes
-     free and bound variables to avoid distinct variable requirements.
+     free and bound variables to avoid distinct variable requirements.  Usage
+     of this theorem is discouraged because it depends on ~ ax-13 .
      (Contributed by NM, 17-Feb-2005.)  (New usage is discouraged.) $)
   dfsb2 $p |- ( [ y / x ] ph <->
               ( ( x = y /\ ph ) \/ A. x ( x = y -> ph ) ) ) $=
@@ -22004,8 +22139,9 @@ requires either a disjoint variable condition ( ~ sb6 ) or a non-freeness
     EAGBABCJKUGUHLMUJTUEUHUIABCNUHUGOPQUGUEUHUFAUEABCRUAABCUBUCUD $.
 
   $( An alternate definition of proper substitution ~ df-sb that uses only
-     primitive connectives (no defined terms) on the right-hand side.
-     (Contributed by NM, 6-Mar-2007.)  (New usage is discouraged.) $)
+     primitive connectives (no defined terms) on the right-hand side.  Usage of
+     this theorem is discouraged because it depends on ~ ax-13 .  (Contributed
+     by NM, 6-Mar-2007.)  (New usage is discouraged.) $)
   dfsb3 $p |- ( [ y / x ] ph <->
               ( ( x = y -> -. ph ) -> A. x ( x = y -> ph ) ) ) $=
     ( weq wa wi wal wo wn wsb df-or dfsb2 imnan imbi1i 3bitr4i ) BCDZAEZPAFBGZH
@@ -22022,8 +22158,9 @@ primitive connectives (no defined terms) on the right-hand side.
     ADBQTUMUOUKAGZDSUIUGUNUQDUGUKUFABDCRUAUBADCUCUDKLUE $.
 
   $( Formula-building lemma for use with the Distinctor Reduction Theorem.
-     Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).  (Contributed
-     by NM, 2-Jun-1993.)  (New usage is discouraged.) $)
+     Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).  Usage of this
+     theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
+     NM, 2-Jun-1993.)  (New usage is discouraged.) $)
   drsb1 $p |- ( A. x x = y -> ( [ z / x ] ph <-> [ z / y ] ph ) ) $=
     ( weq wal wi wa wex wsb wb equequ1 sps imbi1d anbi1d drex1 anbi12d 3bitr4g
     dfsb1 ) BCEZBFZBDEZAGZUBAHZBIZHCDEZAGZUFAHZCIZHABDJACDJUAUCUGUEUIUAUBUFATUB
@@ -22032,8 +22169,9 @@ primitive connectives (no defined terms) on the right-hand side.
   ${
     $d v y $.
     $( In the case of two successive substitutions for two always equal
-       variables, the second substitution has no effect.  (Contributed by BJ
-       and WL, 9-Aug-2023.)  (New usage is discouraged.) $)
+       variables, the second substitution has no effect.  Usage of this theorem
+       is discouraged because it depends on ~ ax-13 .  (Contributed by BJ and
+       WL, 9-Aug-2023.)  (New usage is discouraged.) $)
     sb2ae $p |-
                ( A. x x = y -> ( [ u / x ] [ v / y ] ph <-> [ v / y ] ph ) ) $=
       ( weq wal wsb drsb1 nfs1v sbf syl6bb ) BCFBGACDHZBEHMCEHMMBCEIMCEACDJKL
@@ -22045,8 +22183,10 @@ primitive connectives (no defined terms) on the right-hand side.
     $( Equivalence for substitution when ` y ` is not free in ` ph ` .  The
        implication "to the left" is ~ sb2 and does not require the non-freeness
        hypothesis.  Theorem ~ sb6 replaces the non-freeness hypothesis with a
-       disjoint variable condition.  (Contributed by NM, 2-Jun-1993.)  (Revised
-       by Mario Carneiro, 4-Oct-2016.)  (New usage is discouraged.) $)
+       disjoint variable condition and uses less axioms.  Usage of this theorem
+       is discouraged because it depends on ~ ax-13 .  (Contributed by NM,
+       2-Jun-1993.)  (Revised by Mario Carneiro, 4-Oct-2016.)
+       (New usage is discouraged.) $)
     sb6f $p |- ( [ y / x ] ph <-> A. x ( x = y -> ph ) ) $=
       ( wsb weq wi wal nf5ri sbimi sb4a syl sb2 impbii ) ABCEZBCFAGBHZOACHZBCEP
       AQBCACDIJABCKLABCMN $.
@@ -22054,19 +22194,20 @@ primitive connectives (no defined terms) on the right-hand side.
     $( Equivalence for substitution when ` y ` is not free in ` ph ` .  The
        implication "to the right" is ~ sb1 and does not require the
        non-freeness hypothesis.  Theorem ~ sb5 replaces the non-freeness
-       hypothesis with a disjoint variable condition.  (Contributed by NM,
-       5-Aug-1993.)  (Revised by Mario Carneiro, 4-Oct-2016.)
-       (New usage is discouraged.) $)
+       hypothesis with a disjoint variable condition and uses less axioms.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       (Contributed by NM, 5-Aug-1993.)  (Revised by Mario Carneiro,
+       4-Oct-2016.)  (New usage is discouraged.) $)
     sb5f $p |- ( [ y / x ] ph <-> E. x ( x = y /\ ph ) ) $=
       ( wsb weq wi wal wa wex sb6f equs45f bitr4i ) ABCEBCFZAGBHNAIBJABCDKABCDL
       M $.
   $}
 
   $( A variable not free in a proposition remains so after substitution in that
-     proposition with a distinct variable (closed form of ~ nfsb4 ).
-     (Contributed by NM, 7-Apr-2004.)  (Revised by Mario Carneiro, 4-Oct-2016.)
-     (Proof shortened by Wolf Lammen, 11-May-2018.)
-     (New usage is discouraged.) $)
+     proposition with a distinct variable (closed form of ~ nfsb4 ).  Usage of
+     this theorem is discouraged because it depends on ~ ax-13 .  (Contributed
+     by NM, 7-Apr-2004.)  (Revised by Mario Carneiro, 4-Oct-2016.)  (Proof
+     shortened by Wolf Lammen, 11-May-2018.)  (New usage is discouraged.) $)
   nfsb4t $p |- ( A. x F/ z ph ->
                  ( -. A. z z = y -> F/ z [ y / x ] ph ) ) $=
     ( wnf wal weq wn wsb wi wa sbequ12 sps drnf2 biimpd spsd impcom nfnae nfan
@@ -22078,7 +22219,10 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
   ${
     nfsb4.1 $e |- F/ z ph $.
     $( A variable not free in a proposition remains so after substitution in
-       that proposition with a distinct variable.  (Contributed by NM,
+       that proposition with a distinct variable.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Theorem ~ nfsb replaces the
+       distinctor with a disjoint variable condition.  Visit also ~ nfsbv for a
+       weaker version of ~ nfsb not requiring ~ ax-13 .  (Contributed by NM,
        14-May-1993.)  (Revised by Mario Carneiro, 4-Oct-2016.)
        (New usage is discouraged.) $)
     nfsb4 $p |- ( -. A. z z = y -> F/ z [ y / x ] ph ) $=
@@ -22105,10 +22249,11 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     KLMUBNZUEUAAGZCFZUDUFACDOUHUDUAUCGZCFZUJUFGUCCDOULUJUABGZCFUFUKUIUMCUAABSPB
     CDQTTJR $.
 
-  $( Elimination of equality from antecedent after substitution.  (Contributed
-     by NM, 5-Aug-1993.)  Reduce dependencies on axioms.  (Revised by Wolf
-     Lammen, 28-Jul-2018.)  Revise ~ df-sb .  (Revised by Wolf Lammen,
-     28-Jul-2023.)  (New usage is discouraged.) $)
+  $( Elimination of equality from antecedent after substitution.  Usage of this
+     theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
+     NM, 5-Aug-1993.)  Reduce dependencies on axioms.  (Revised by Wolf Lammen,
+     28-Jul-2018.)  Revise ~ df-sb .  (Revised by Wolf Lammen, 28-Jul-2023.)
+     (New usage is discouraged.) $)
   sbequ8 $p |- ( [ y / x ] ph <-> [ y / x ] ( x = y -> ph ) ) $=
     ( wsb weq wi equsb1 a1bi sbim bitr4i ) ABCDZBCEZBCDZKFLAFBCDMKBCGHLABCIJ $.
 
@@ -22117,7 +22262,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     sbie.2 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Conversion of implicit substitution to explicit substitution.  For
        versions requiring disjoint variables, but fewer axioms, see ~ sbiev and
-       ~ sbievw .  (Contributed by NM, 30-Jun-1994.)  (Revised by Mario
+       ~ sbievw .  Usage of this theorem is discouraged because it depends on
+       ~ ax-13 .  (Contributed by NM, 30-Jun-1994.)  (Revised by Mario
        Carneiro, 4-Oct-2016.)  (Proof shortened by Wolf Lammen, 13-Jul-2019.)
        (New usage is discouraged.) $)
     sbie $p |- ( [ y / x ] ph <-> ps ) $=
@@ -22130,8 +22276,9 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     sbied.2 $e |- ( ph -> F/ x ch ) $.
     sbied.3 $e |- ( ph -> ( x = y -> ( ps <-> ch ) ) ) $.
     $( Conversion of implicit substitution to explicit substitution (deduction
-       version of ~ sbie ) See ~ sbiedv , ~ sbiedw , ~ sbiedvw for variants
-       using disjoint variables, but require fewer axioms.  (Contributed by NM,
+       version of ~ sbie ) Usage of this theorem is discouraged because it
+       depends on ~ ax-13 .  See ~ sbiedw , ~ sbiedvw for variants using
+       disjoint variables, but requiring fewer axioms.  (Contributed by NM,
        30-Jun-1994.)  (Revised by Mario Carneiro, 4-Oct-2016.)  (Proof
        shortened by Wolf Lammen, 24-Jun-2018.)  (New usage is discouraged.) $)
     sbied $p |- ( ph -> ( [ y / x ] ps <-> ch ) ) $=
@@ -22143,9 +22290,9 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $d x ph $.  $d x ch $.
     sbiedv.1 $e |- ( ( ph /\ x = y ) -> ( ps <-> ch ) ) $.
     $( Conversion of implicit substitution to explicit substitution (deduction
-       version of ~ sbie ).  See ~ sbied , ~ sbiedvw , ~ sbiedw for similar
-       variants (Contributed by NM, 7-Jan-2017.)
-       (New usage is discouraged.) $)
+       version of ~ sbie ).  Usage of this theorem is discouraged because it
+       depends on ~ ax-13 .  Use the weaker ~ sbiedvw when possible.
+       (Contributed by NM, 7-Jan-2017.)  (New usage is discouraged.) $)
     sbiedv $p |- ( ph -> ( [ y / x ] ps <-> ch ) ) $=
       ( nfv nfvd weq wb ex sbied ) ABCDEADGACDHADEIBCJFKL $.
   $}
@@ -22154,7 +22301,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $d x y ps $.  $d t y $.
     2sbiev.1 $e |- ( ( x = t /\ y = u ) -> ( ph <-> ps ) ) $.
     $( Conversion of double implicit substitution to explicit substitution.
-       See ~ 2sbievw for a variant with extra disjoint variables, but based on
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       See ~ 2sbievw for a version with extra disjoint variables, but based on
        fewer axioms.  (Contributed by AV, 29-Jul-2023.)
        (New usage is discouraged.) $)
     2sbiev $p |- ( [ t / x ] [ u / y ] ph <-> ps ) $=
@@ -22162,8 +22310,9 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
   $}
 
   $( Substituting ` y ` for ` x ` and then ` z ` for ` y ` is equivalent to
-     substituting ` z ` for both ` x ` and ` y ` .  For a version requiring
-     disjoint variables, but fewer axioms, see ~ sbcom3vv .  (Contributed by
+     substituting ` z ` for both ` x ` and ` y ` .  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  For a version requiring a
+     disjoint variable, but fewer axioms, see ~ sbcom3vv .  (Contributed by
      Giovanni Mascellani, 8-Apr-2018.)  Remove dependency on ~ ax-11 .
      (Revised by Wolf Lammen, 16-Sep-2018.)  (Proof shortened by Wolf Lammen,
      16-Sep-2018.)  (New usage is discouraged.) $)
@@ -22172,8 +22321,9 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     wi pm2.61i ) CDEZCFZABCGZCDGZABDGZCDGZHUBUCUECDUACIACDBJKUBLZUDUAUESZCFZUFU
     GUDUAUCSZCFUIUCCDMUJUHCUAUCUEACDBNOPQUECDMRT $.
 
-  $( A composition law for substitution.  See ~ sbcov for a version with a
-     disjoint variable condition requiring fewer axioms.  (Contributed by NM,
+  $( A composition law for substitution.  Usage of this theorem is discouraged
+     because it depends on ~ ax-13 .  See ~ sbcov for a version with a disjoint
+     variable condition requiring fewer axioms.  (Contributed by NM,
      14-May-1993.)  (Proof shortened by Wolf Lammen, 21-Sep-2018.)
      (New usage is discouraged.) $)
   sbco $p |- ( [ y / x ] [ x / y ] ph <-> [ y / x ] ph ) $=
@@ -22181,7 +22331,9 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
 
   ${
     sbid2.1 $e |- F/ x ph $.
-    $( An identity law for substitution.  (Contributed by NM, 14-May-1993.)
+    $( An identity law for substitution.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Check out ~ sbid2vw for a weaker
+       version requiring fewer axioms.  (Contributed by NM, 14-May-1993.)
        (Revised by Mario Carneiro, 6-Oct-2016.)  (New usage is discouraged.) $)
     sbid2 $p |- ( [ y / x ] [ x / y ] ph <-> ph ) $=
       ( wsb sbco sbf bitri ) ACBEBCEABCEAABCFABCDGH $.
@@ -22190,15 +22342,17 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
   ${
     $d x ph $.
     $( An identity law for substitution.  Used in proof of Theorem 9.7 of
-       [Megill] p. 449 (p. 16 of the preprint).  See ~ sbid2vw for a version
-       with a disjoint variable condition requiring fewer axioms.  (Contributed
-       by NM, 5-Aug-1993.)  (New usage is discouraged.) $)
+       [Megill] p. 449 (p. 16 of the preprint).  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  See ~ sbid2vw for a version
+       with an extra disjoint variable condition requiring fewer axioms.
+       (Contributed by NM, 5-Aug-1993.)  (New usage is discouraged.) $)
     sbid2v $p |- ( [ y / x ] [ x / y ] ph <-> ph ) $=
       ( nfv sbid2 ) ABCABDE $.
   $}
 
-  $( An idempotent law for substitution.  (Contributed by NM, 30-Jun-1994.)
-     (Proof shortened by Andrew Salmon, 25-May-2011.)  (Proof shortened by Wolf
+  $( An idempotent law for substitution.  Usage of this theorem is discouraged
+     because it depends on ~ ax-13 .  (Contributed by NM, 30-Jun-1994.)  (Proof
+     shortened by Andrew Salmon, 25-May-2011.)  (Proof shortened by Wolf
      Lammen, 13-Jul-2019.)  (New usage is discouraged.) $)
   sbidm $p |- ( [ y / x ] [ y / x ] ph <-> [ y / x ] ph ) $=
     ( wsb sbcom3 sbid sbbii bitr3i ) ABCDZBCDABBDZBCDIABBCEJABCABFGH $.
@@ -22207,7 +22361,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     sbco2.1 $e |- F/ z ph $.
     $( A composition law for substitution.  For versions requiring fewer
        axioms, but more disjoint variable conditions, see ~ sbco2v and
-       ~ sbco2vv .  (Contributed by NM, 30-Jun-1994.)  (Revised by Mario
+       ~ sbco2vv .  Usage of this theorem is discouraged because it depends on
+       ~ ax-13 .  (Contributed by NM, 30-Jun-1994.)  (Revised by Mario
        Carneiro, 6-Oct-2016.)  (Proof shortened by Wolf Lammen, 17-Sep-2018.)
        (New usage is discouraged.) $)
     sbco2 $p |- ( [ y / z ] [ z / x ] ph <-> [ y / x ] ph ) $=
@@ -22220,33 +22375,37 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     sbco2d.1 $e |- F/ x ph $.
     sbco2d.2 $e |- F/ z ph $.
     sbco2d.3 $e |- ( ph -> F/ z ps ) $.
-    $( A composition law for substitution.  (Contributed by NM, 2-Jun-1993.)
-       (Revised by Mario Carneiro, 6-Oct-2016.)  (New usage is discouraged.) $)
+    $( A composition law for substitution.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  (Contributed by NM,
+       2-Jun-1993.)  (Revised by Mario Carneiro, 6-Oct-2016.)
+       (New usage is discouraged.) $)
     sbco2d $p |- ( ph -> ( [ y / z ] [ z / x ] ps <-> [ y / x ] ps ) ) $=
       ( wsb wi nfim1 sbco2 sbrim sbbii bitri 3bitr3i pm5.74ri ) ABCEIZEDIZBCDIZ
       ABJZCEIZEDIZUACDIASJZATJUACDEABEGHKLUCARJZEDIUDUBUEEDABCEFMNAREDGMOABCDFM
       PQ $.
   $}
 
-  $( A composition law for substitution.  (Contributed by NM, 2-Jun-1993.)
-     (Proof shortened by Wolf Lammen, 18-Sep-2018.)
-     (New usage is discouraged.) $)
+  $( A composition law for substitution.  Usage of this theorem is discouraged
+     because it depends on ~ ax-13 .  (Contributed by NM, 2-Jun-1993.)  (Proof
+     shortened by Wolf Lammen, 18-Sep-2018.)  (New usage is discouraged.) $)
   sbco3 $p |- ( [ z / y ] [ y / x ] ph <-> [ z / x ] [ x / y ] ph ) $=
     ( weq wal wsb wb drsb1 nfae sbequ12a sbbid bitr3d wn sbco sbbii nfnae nfsb2
     sps sbco2d syl5rbbr pm2.61i ) BCEZBFZABCGZCDGZACBGZBDGZHUDUEBDGUFUHUEBCDIUD
     UEUGBDBCBJUCUEUGHBABCKSLMUHUECBGZBDGUDNZUFUIUGBDACBOPUJUECDBBCCQBCBQABCRTUA
     UB $.
 
-  $( A commutativity law for substitution.  (Contributed by NM, 27-May-1997.)
-     (Proof shortened by Wolf Lammen, 20-Sep-2018.)
-     (New usage is discouraged.) $)
+  $( A commutativity law for substitution.  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  Check out ~ sbcom3vv for a
+     version requiring less axioms.  (Contributed by NM, 27-May-1997.)  (Proof
+     shortened by Wolf Lammen, 20-Sep-2018.)  (New usage is discouraged.) $)
   sbcom $p |- ( [ y / z ] [ y / x ] ph <-> [ y / x ] [ y / z ] ph ) $=
     ( wsb sbco3 sbcom3 3bitr3i ) ABDEDCEADBEBCEABCEDCEADCEBCEABDCFABDCGADBCGH
     $.
 
   ${
     sbtrt.nf $e |- F/ y ph $.
-    $( Partially closed form of ~ sbtr .  (Contributed by BJ, 4-Jun-2019.)
+    $( Partially closed form of ~ sbtr .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by BJ, 4-Jun-2019.)
        (New usage is discouraged.) $)
     sbtrt $p |- ( A. y [ y / x ] ph -> ph ) $=
       ( wsb wal stdpc4 sbid2 sylib ) ABCEZCFJCBEAJCBGACBDHI $.
@@ -22257,7 +22416,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     sbtr.1 $e |- [ y / x ] ph $.
     $( A partial converse to ~ sbt .  If the substitution of a variable for a
        non-free one in a wff gives a theorem, then the original wff is a
-       theorem.  (Contributed by BJ, 15-Sep-2018.)
+       theorem.  Usage of this theorem is discouraged because it depends on
+       ~ ax-13 .  (Contributed by BJ, 15-Sep-2018.)
        (New usage is discouraged.) $)
     sbtr $p |- ph $=
       ( wsb sbtrt mpg ) ABCFACABCDGEH $.
@@ -22265,15 +22425,16 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
 
   ${
     sb8.1 $e |- F/ y ph $.
-    $( Substitution of variable in universal quantifier.  For a version
-       requiring disjoint variables, but fewer axioms, see ~ sb8v .
-       (Contributed by NM, 16-May-1993.)  (Revised by Mario Carneiro,
-       6-Oct-2016.)  (Proof shortened by Jim Kingdon, 15-Jan-2018.)
-       (New usage is discouraged.) $)
+    $( Substitution of variable in universal quantifier.  Usage of this theorem
+       is discouraged because it depends on ~ ax-13 .  For a version requiring
+       disjoint variables, but fewer axioms, see ~ sb8v .  (Contributed by NM,
+       16-May-1993.)  (Revised by Mario Carneiro, 6-Oct-2016.)  (Proof
+       shortened by Jim Kingdon, 15-Jan-2018.)  (New usage is discouraged.) $)
     sb8 $p |- ( A. x ph <-> A. y [ y / x ] ph ) $=
       ( wsb nfs1 sbequ12 cbval ) AABCEBCDABCDFABCGH $.
 
-    $( Substitution of variable in existential quantifier.  For a version
+    $( Substitution of variable in existential quantifier.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  For a version
        requiring disjoint variables, but fewer axioms, see ~ sb8ev .
        (Contributed by NM, 12-Aug-1993.)  (Revised by Mario Carneiro,
        6-Oct-2016.)  (Proof shortened by Jim Kingdon, 15-Jan-2018.)
@@ -22282,7 +22443,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
       ( wsb nfs1 sbequ12 cbvex ) AABCEBCDABCDFABCGH $.
   $}
 
-  $( Commutation of quantification and substitution variables.  (Contributed by
+  $( Commutation of quantification and substitution variables.  Usage of this
+     theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
      NM, 5-Aug-1993.)  Allow a shortening of ~ sb9i .  (Revised by Wolf Lammen,
      15-Jun-2019.)  (New usage is discouraged.) $)
   sb9 $p |- ( A. x [ x / y ] ph <-> A. y [ y / x ] ph ) $=
@@ -22290,7 +22452,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     wi a1i pm2.61i ) BCDZBEZACBFZBEABCFZCEGUCUDBCUAUCUDGZBUECBACBHIZJKUBLZUCUDB
     CBCBMBCCMUCCNCBACBOPABCOUAUERUGUFSQT $.
 
-  $( Commutation of quantification and substitution variables.  (Contributed by
+  $( Commutation of quantification and substitution variables.  Usage of this
+     theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
      NM, 5-Aug-1993.)  (Proof shortened by Wolf Lammen, 15-Jun-2019.)
      (New usage is discouraged.) $)
   sb9i $p |- ( A. x [ x / y ] ph -> A. y [ y / x ] ph ) $=
@@ -22299,6 +22462,7 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
   ${
     $d y ph $.
     $( Two ways of expressing " ` x ` is (effectively) not free in ` ph ` ".
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 29-May-2009.)  (New usage is discouraged.) $)
     sbhb $p |- ( ( ph -> A. x ph ) <-> A. y ( ph -> [ y / x ] ph ) ) $=
       ( wal wi wsb nfv sb8 imbi2i 19.21v bitr4i ) AABDZEAABCFZCDZEAMECDLNAABCAC
@@ -22309,7 +22473,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $d y z $.
     nfsbd.1 $e |- F/ x ph $.
     nfsbd.2 $e |- ( ph -> F/ z ps ) $.
-    $( Deduction version of ~ nfsb .  (Contributed by NM, 15-Feb-2013.)
+    $( Deduction version of ~ nfsb .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by NM, 15-Feb-2013.)
        (New usage is discouraged.) $)
     nfsbd $p |- ( ph -> F/ z [ y / x ] ps ) $=
       ( weq wal wsb wnf wn wi alrimi nfsb4t syl axc16nf pm2.61d2 ) AEDHEIZBCDJZ
@@ -22320,7 +22485,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $d y z $.
     nfsb.1 $e |- F/ z ph $.
     $( If ` z ` is not free in ` ph ` , it is not free in ` [ y / x ] ph ` when
-       ` y ` and ` z ` are distinct.  For a version requiring more disjoint
+       ` y ` and ` z ` are distinct.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  For a version requiring more disjoint
        variables, but fewer axioms, see ~ nfsbv .  (Contributed by Mario
        Carneiro, 11-Aug-2016.)  (Proof shortened by Wolf Lammen, 25-Feb-2024.)
        (New usage is discouraged.) $)
@@ -22338,8 +22504,9 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     $d y z $.
     hbsb.1 $e |- ( ph -> A. z ph ) $.
     $( If ` z ` is not free in ` ph ` , it is not free in ` [ y / x ] ph ` when
-       ` y ` and ` z ` are distinct.  (Contributed by NM, 12-Aug-1993.)
-       (New usage is discouraged.) $)
+       ` y ` and ` z ` are distinct.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ hbsbw when possible.
+       (Contributed by NM, 12-Aug-1993.)  (New usage is discouraged.) $)
     hbsb $p |- ( [ y / x ] ph -> A. z [ y / x ] ph ) $=
       ( wsb nf5i nfsb nf5ri ) ABCFDABCDADEGHI $.
   $}
@@ -22352,7 +22519,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
        in a formalization that omits the logically redundant axiom ~ ax-5 i.e.
        that doesn't have the concept of a variable not occurring in a wff.
        ( ~ dfsb1 is also suitable, but its mixing of free and bound variables
-       is distasteful to some logicians.)  (Contributed by NM, 26-Jul-2006.)
+       is distasteful to some logicians.)  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by NM, 26-Jul-2006.)
        (Revised by Mario Carneiro, 6-Oct-2016.)  (New usage is discouraged.) $)
     sb7f $p |- ( [ y / x ] ph <->
                E. z ( z = y /\ E. x ( x = z /\ ph ) ) ) $=
@@ -22368,7 +22536,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
        in a formalization that omits the logically redundant axiom ~ ax-5 i.e.
        that doesn't have the concept of a variable not occurring in a wff.
        ( ~ dfsb1 is also suitable, but its mixing of free and bound variables
-       is distasteful to some logicians.)  (Contributed by NM, 26-Jul-2006.)
+       is distasteful to some logicians.)  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by NM, 26-Jul-2006.)
        (Proof shortened by Andrew Salmon, 25-May-2011.)
        (New usage is discouraged.) $)
     sb7h $p |- ( [ y / x ] ph <->
@@ -22401,7 +22570,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
     sb10f.1 $e |- F/ x ph $.
     $( Hao Wang's identity axiom P6 in Irving Copi, _Symbolic Logic_ (5th ed.,
        1979), p. 328.  In traditional predicate calculus, this is a sole axiom
-       for identity from which the usual ones can be derived.  (Contributed by
+       for identity from which the usual ones can be derived.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
        NM, 9-May-2005.)  (Revised by Mario Carneiro, 6-Oct-2016.)
        (New usage is discouraged.) $)
     sb10f $p |- ( [ y / z ] ph <-> E. x ( x = y /\ [ x / z ] ph ) ) $=
@@ -22428,9 +22598,12 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
 
   ${
     $d z x $.
-    $( Move quantifier in and out of substitution.  (Contributed by NM,
-       2-Jan-2002.)  Remove a distinct variable constraint.  (Revised by Wolf
-       Lammen, 24-Dec-2022.)  (Proof shortened by Wolf Lammen, 23-Sep-2023.)
+    $( Move quantifier in and out of substitution.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Check out ~ sbal for a
+       version replacing the distinctor with a disjoint variable condition,
+       requiring fewer axioms.  (Contributed by NM, 2-Jan-2002.)  Remove a
+       distinct variable constraint.  (Revised by Wolf Lammen, 24-Dec-2022.)
+       (Proof shortened by Wolf Lammen, 23-Sep-2023.)
        (New usage is discouraged.) $)
     sbal2 $p |- ( -. A. x x = y ->
              ( [ z / y ] A. x ph <-> A. x [ z / y ] ph ) ) $=
@@ -22467,7 +22640,8 @@ proposition with a distinct variable (closed form of ~ nfsb4 ).
 
   ${
     $d z w ph $.
-    $( An equivalent expression for double existence.  For a version requiring
+    $( An equivalent expression for double existence.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  For a version requiring
        more disjoint variables, but fewer axioms, see ~ 2sb8ev .  (Contributed
        by Wolf Lammen, 2-Nov-2019.)  (New usage is discouraged.) $)
     2sb8e $p |- ( E. x E. y ph <->
@@ -23112,9 +23286,12 @@ derived from that of uniqueness ( ~ df-mo ).  (Contributed by Wolf
     $d x z $.  $d y z $.  $d z ph $.  $d z ps $.
     nfmod2.1 $e |- F/ y ph $.
     nfmod2.2 $e |- ( ( ph /\ -. A. x x = y ) -> F/ x ps ) $.
-    $( Bound-variable hypothesis builder for the at-most-one quantifier.
-       (Contributed by Mario Carneiro, 14-Nov-2016.)  Avoid ~ df-eu .  (Revised
-       by BJ, 14-Oct-2022.)  (New usage is discouraged.) $)
+    $( Bound-variable hypothesis builder for the at-most-one quantifier.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  See
+       ~ nfmodv for a version replacing the distinctor with a disjoint variable
+       condition, not requiring ~ ax-13 .  (Contributed by Mario Carneiro,
+       14-Nov-2016.)  Avoid ~ df-eu .  (Revised by BJ, 14-Oct-2022.)
+       (New usage is discouraged.) $)
     nfmod2 $p |- ( ph -> F/ x E* y ps ) $=
       ( vz wmo weq wi wal wex df-mo nfv wn wa wnf nfeqf1 adantl nfimd nfald2
       nfexd nfxfrd ) BDHBDGIZJZDKZGLACBDGMAUFCGAGNAUECDEACDICKOZPBUDCFUGUDCQACD
@@ -23149,8 +23326,10 @@ derived from that of uniqueness ( ~ df-mo ).  (Contributed by Wolf
     nfmod.1 $e |- F/ y ph $.
     nfmod.2 $e |- ( ph -> F/ x ps ) $.
     $( Bound-variable hypothesis builder for the at-most-one quantifier.
-       Deduction version of ~ nfmo .  (Contributed by Mario Carneiro,
-       14-Nov-2016.)  (New usage is discouraged.) $)
+       Deduction version of ~ nfmo .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ nfmodv when possible.
+       (Contributed by Mario Carneiro, 14-Nov-2016.)
+       (New usage is discouraged.) $)
     nfmod $p |- ( ph -> F/ x E* y ps ) $=
       ( wnf weq wal wn adantr nfmod2 ) ABCDEABCGCDHCIJFKL $.
   $}
@@ -23158,8 +23337,10 @@ derived from that of uniqueness ( ~ df-mo ).  (Contributed by Wolf
   ${
     nfmo.1 $e |- F/ x ph $.
     $( Bound-variable hypothesis builder for the at-most-one quantifier.  Note
-       that ` x ` and ` y ` need not be disjoint.  (Contributed by NM,
-       9-Mar-1995.)  (New usage is discouraged.) $)
+       that ` x ` and ` y ` need not be disjoint.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ nfmov when
+       possible.  (Contributed by NM, 9-Mar-1995.)
+       (New usage is discouraged.) $)
     nfmo $p |- F/ x E* y ph $=
       ( wmo wnf wtru nftru a1i nfmod mptru ) ACEBFGABCCHABFGDIJK $.
   $}
@@ -23498,9 +23679,12 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
   ${
     nfeud2.1 $e |- F/ y ph $.
     nfeud2.2 $e |- ( ( ph /\ -. A. x x = y ) -> F/ x ps ) $.
-    $( Bound-variable hypothesis builder for uniqueness.  (Contributed by Mario
-       Carneiro, 14-Nov-2016.)  (Proof shortened by Wolf Lammen, 4-Oct-2018.)
-       (Proof shortened by BJ, 14-Oct-2022.)  (New usage is discouraged.) $)
+    $( Bound-variable hypothesis builder for uniqueness.  Usage of this theorem
+       is discouraged because it depends on ~ ax-13 .  Check out ~ nfeudw for a
+       version that replaces the distinctor with a disjoint variable condition,
+       not requiring ~ ax-13 .  (Contributed by Mario Carneiro, 14-Nov-2016.)
+       (Proof shortened by Wolf Lammen, 4-Oct-2018.)  (Proof shortened by BJ,
+       14-Oct-2022.)  (New usage is discouraged.) $)
     nfeud2 $p |- ( ph -> F/ x E! y ps ) $=
       ( weu wex wmo wa df-eu nfexd2 nfmod2 nfand nfxfrd ) BDGBDHZBDIZJACBDKAPQC
       ABCDEFLABCDEFMNO $.
@@ -23522,8 +23706,10 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     nfeud.1 $e |- F/ y ph $.
     nfeud.2 $e |- ( ph -> F/ x ps ) $.
     $( Bound-variable hypothesis builder for the unique existential quantifier.
-       Deduction version of ~ nfeu .  (Contributed by NM, 15-Feb-2013.)
-       (Revised by Mario Carneiro, 7-Oct-2016.)  (New usage is discouraged.) $)
+       Deduction version of ~ nfeu .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ nfeudw when possible.
+       (Contributed by NM, 15-Feb-2013.)  (Revised by Mario Carneiro,
+       7-Oct-2016.)  (New usage is discouraged.) $)
     nfeud $p |- ( ph -> F/ x E! y ps ) $=
       ( wnf weq wal wn adantr nfeud2 ) ABCDEABCGCDHCIJFKL $.
   $}
@@ -23541,9 +23727,10 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
   ${
     nfeu.1 $e |- F/ x ph $.
     $( Bound-variable hypothesis builder for the unique existential quantifier.
-       Note that ` x ` and ` y ` need not be disjoint.  (Contributed by NM,
-       8-Mar-1995.)  (Revised by Mario Carneiro, 7-Oct-2016.)
-       (New usage is discouraged.) $)
+       Note that ` x ` and ` y ` need not be disjoint.  Usage of this theorem
+       is discouraged because it depends on ~ ax-13 .  Use the weaker ~ nfeuw
+       when possible.  (Contributed by NM, 8-Mar-1995.)  (Revised by Mario
+       Carneiro, 7-Oct-2016.)  (New usage is discouraged.) $)
     nfeu $p |- F/ x E! y ph $=
       ( weu wnf wtru nftru a1i nfeud mptru ) ACEBFGABCCHABFGDIJK $.
   $}
@@ -23605,12 +23792,14 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
        (Contributed by Wolf Lammen, 7-Feb-2023.) $)
     sb8euv $p |- ( E! x ph <-> E! y [ y / x ] ph ) $=
       ( vw nfsbv sb8eulem ) ABCEABECDFG $.
+    $( $j usage 'sb8euv' avoids 'ax-13'; $)
   $}
 
   ${
     $d w y $.  $d ph w $.  $d w x $.
     sb8eu.1 $e |- F/ y ph $.
-    $( Variable substitution in unique existential quantifier.  For a version
+    $( Variable substitution in unique existential quantifier.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  For a version
        requiring more disjoint variables, but fewer axioms, see ~ sb8euv .
        (Contributed by NM, 7-Aug-1994.)  (Revised by Mario Carneiro,
        7-Oct-2016.)  (Proof shortened by Wolf Lammen, 24-Aug-2019.)
@@ -23618,7 +23807,8 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     sb8eu $p |- ( E! x ph <-> E! y [ y / x ] ph ) $=
       ( vw nfsb sb8eulem ) ABCEABECDFG $.
 
-    $( Variable substitution for the at-most-one quantifier.  (Contributed by
+    $( Variable substitution for the at-most-one quantifier.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
        Alexander van der Vekens, 17-Jun-2017.)  (New usage is discouraged.) $)
     sb8mo $p |- ( E* x ph <-> E* y [ y / x ] ph ) $=
       ( wex weu wi wsb wmo sb8e sb8eu imbi12i moeu 3bitr4i ) ABEZABFZGABCHZCEZQ
@@ -23643,10 +23833,11 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     cbvmo.1 $e |- F/ y ph $.
     cbvmo.2 $e |- F/ x ps $.
     cbvmo.3 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 9-Mar-1995.)  (Revised by Andrew Salmon,
-       8-Jun-2011.)  (Proof shortened by Wolf Lammen, 4-Jan-2023.)
-       (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ cbvmow when possible.  (Contributed by NM, 9-Mar-1995.)
+       (Revised by Andrew Salmon, 8-Jun-2011.)  (Proof shortened by Wolf
+       Lammen, 4-Jan-2023.)  (New usage is discouraged.) $)
     cbvmo $p |- ( E* x ph <-> E* y ps ) $=
       ( wmo wsb sb8mo sbie mobii bitri ) ACHACDIZDHBDHACDEJNBDABCDFGKLM $.
   $}
@@ -23667,9 +23858,10 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     cbveu.1 $e |- F/ y ph $.
     cbveu.2 $e |- F/ x ps $.
     cbveu.3 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 25-Nov-1994.)  (Revised by Mario Carneiro,
-       7-Oct-2016.)  (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ cbveuw when possible.  (Contributed by NM, 25-Nov-1994.)
+       (Revised by Mario Carneiro, 7-Oct-2016.)  (New usage is discouraged.) $)
     cbveu $p |- ( E! x ph <-> E! y ps ) $=
       ( weu wsb sb8eu sbie eubii bitri ) ACHACDIZDHBDHACDEJNBDABCDFGKLM $.
 
@@ -23962,9 +24154,11 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
 
   ${
     moexex.1 $e |- F/ y ph $.
-    $( "At most one" double quantification.  (Contributed by NM, 3-Dec-2001.)
-       (Proof shortened by Wolf Lammen, 28-Dec-2018.)  Factor out common proof
-       lines with ~ moexexvw .  (Revised by Wolf Lammen, 2-Oct-2023.)
+    $( "At most one" double quantification.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the version ~ moexexvw
+       when possible.  (Contributed by NM, 3-Dec-2001.)  (Proof shortened by
+       Wolf Lammen, 28-Dec-2018.)  Factor out common proof lines with
+       ~ moexexvw .  (Revised by Wolf Lammen, 2-Oct-2023.)
        (New usage is discouraged.) $)
     moexex $p |- ( ( E* x ph /\ A. x E* y ps ) -> E* y E. x ( ph /\ ps ) ) $=
       ( nfmo wa wex nfe1 moexexlem ) ABCDEADCEFABGZCHCDKCIFJ $.
@@ -23972,20 +24166,25 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
 
   ${
     $d y ph $.
-    $( "At most one" double quantification.  (Contributed by NM, 26-Jan-1997.)
+    $( "At most one" double quantification.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ moexexvw
+       when possible.  (Contributed by NM, 26-Jan-1997.)
        (New usage is discouraged.) $)
     moexexv $p |- ( ( E* x ph /\ A. x E* y ps ) -> E* y E. x ( ph /\ ps ) ) $=
       ( nfv moexex ) ABCDADEF $.
   $}
 
-  $( Double quantification with "at most one".  (Contributed by NM,
-     3-Dec-2001.)  (New usage is discouraged.) $)
+  $( Double quantification with "at most one".  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  Use the weaker ~ 2moexv when
+     possible.  (Contributed by NM, 3-Dec-2001.)
+     (New usage is discouraged.) $)
   2moex $p |- ( E* x E. y ph -> A. y E* x ph ) $=
     ( wex wmo nfe1 nfmo 19.8a moimi alrimi ) ACDZBEABECKCBACFGAKBACHIJ $.
 
-  $( Double quantification with existential uniqueness.  (Contributed by NM,
-     3-Dec-2001.)  (Proof shortened by Andrew Salmon, 9-Jul-2011.)
-     (New usage is discouraged.) $)
+  $( Double quantification with existential uniqueness.  Usage of this theorem
+     is discouraged because it depends on ~ ax-13 .  Use the weaker ~ 2euexv
+     when possible.  (Contributed by NM, 3-Dec-2001.)  (Proof shortened by
+     Andrew Salmon, 9-Jul-2011.)  (New usage is discouraged.) $)
   2euex $p |- ( E! x E. y ph -> E. y E! x ph ) $=
     ( wex weu wmo wa df-eu excom nfe1 nfmo 19.8a moimi moeu sylib syl5bi impcom
     wi eximd sylbi ) ACDZBEUABDZUABFZGABEZCDZUABHUCUBUEUBABDZCDUCUEABCIUCUFUDCU
@@ -24001,23 +24200,26 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     ( weu wex euex eximi syl ) ACDZBDIBEACEZBEIBFIJBACFGH $.
 
   $( A condition allowing to swap an existential quantifier and at at-most-one
-     quantifier.  (Contributed by NM, 10-Apr-2004.)
-     (New usage is discouraged.) $)
+     quantifier.  Usage of this theorem is discouraged because it depends on
+     ~ ax-13 .  Use the weaker ~ 2moswapv when possible.  (Contributed by NM,
+     10-Apr-2004.)  (New usage is discouraged.) $)
   2moswap $p |- ( A. x E* y ph -> ( E* x E. y ph -> E* y E. x ph ) ) $=
     ( wmo wal wex wa nfe1 moexex expcom 19.8a pm4.71ri exbii mobii syl6ibr ) AC
     DBEZACFZBDZQAGZBFZCDZABFZCDRPUAQABCACHIJUBTCASBAQACKLMNO $.
 
   $( A condition allowing to swap an existential quantifier and a unique
-     existential quantifier.  (Contributed by NM, 10-Apr-2004.)
-     (New usage is discouraged.) $)
+     existential quantifier.  Usage of this theorem is discouraged because it
+     depends on ~ ax-13 .  Use the weaker ~ 2euswapv when possible.
+     (Contributed by NM, 10-Apr-2004.)  (New usage is discouraged.) $)
   2euswap $p |- ( A. x E* y ph -> ( E! x E. y ph -> E! y E. x ph ) ) $=
     ( wmo wal wex wa weu wi excomim a1i 2moswap anim12d df-eu 3imtr4g ) ACDBEZA
     CFZBFZQBDZGABFZCFZTCDZGQBHTCHPRUASUBRUAIPABCJKABCLMQBNTCNO $.
 
   $( Double existential uniqueness implies double unique existential
-     quantification.  The converse does not hold.  (Contributed by NM,
-     3-Dec-2001.)  (Proof shortened by Mario Carneiro, 22-Dec-2016.)
-     (New usage is discouraged.) $)
+     quantification.  The converse does not hold.  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  Use the weaker ~ 2exeuv when
+     possible.  (Contributed by NM, 3-Dec-2001.)  (Proof shortened by Mario
+     Carneiro, 22-Dec-2016.)  (New usage is discouraged.) $)
   2exeu $p |- ( ( E! x E. y ph /\ E! y E. x ph ) -> E! x E! y ph ) $=
     ( wex weu wa wmo eumo euex moimi syl 2euex anim12ci df-eu sylibr ) ACDZBEZA
     BDCEZFACEZBDZSBGZFSBEQUARTQPBGUAPBHSPBACIJKACBLMSBNO $.
@@ -24075,9 +24277,10 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
   $}
 
   $( Double existential uniqueness.  This theorem shows a condition under which
-     a "naive" definition matches the correct one.  (Contributed by NM,
-     3-Dec-2001.)  (Proof shortened by Wolf Lammen, 23-Apr-2023.)
-     (New usage is discouraged.) $)
+     a "naive" definition matches the correct one.  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  Use the weaker ~ 2eu1v when
+     possible.  (Contributed by NM, 3-Dec-2001.)  (Proof shortened by Wolf
+     Lammen, 23-Apr-2023.)  (New usage is discouraged.) $)
   2eu1 $p |- ( A. x E* y ph ->
         ( E! x E! y ph <-> ( E! x E. y ph /\ E! y E. x ph ) ) ) $=
     ( wmo wal weu wex wa wi 2eu2ex moeu albii euim sylan2b pm2.43b 2euswap syld
@@ -24108,14 +24311,16 @@ of the unique existential quantifier (note that ` y ` and ` z ` need not
     $( $j usage '2eu1v' avoids 'ax-13'; $)
   $}
 
-  $( Double existential uniqueness.  (Contributed by NM, 3-Dec-2001.)
+  $( Double existential uniqueness.  Usage of this theorem is discouraged
+     because it depends on ~ ax-13 .  (Contributed by NM, 3-Dec-2001.)
      (New usage is discouraged.) $)
   2eu2 $p |- ( E! y E. x ph -> ( E! x E! y ph <-> E! x E. y ph ) ) $=
     ( wex weu wmo wal wi eumo 2moex 2eu1 simpl syl6bi 3syl 2exeu expcom impbid
     wa ) ABDZCEZACEBEZACDBEZTSCFACFBGZUAUBHSCIACBJUCUAUBTRUBABCKUBTLMNUBTUAABCO
     PQ $.
 
-  $( Double existential uniqueness.  (Contributed by NM, 3-Dec-2001.)  (Proof
+  $( Double existential uniqueness.  Usage of this theorem is discouraged
+     because it depends on ~ ax-13 .  (Contributed by NM, 3-Dec-2001.)  (Proof
      shortened by Wolf Lammen, 23-Apr-2023.)  (New usage is discouraged.) $)
   2eu3 $p |- ( A. x A. y ( E* x ph \/ E* y ph ) ->
  ( ( E! x E! y ph /\ E! y E! x ph ) <-> ( E! x E. y ph /\ E! y E. x ph ) ) ) $=
@@ -24197,8 +24402,9 @@ correct definition apparently has never been published ( ` E* ` means
       TVHVIVJ $.
   $}
 
-  $( Two equivalent expressions for double existential uniqueness.
-     (Contributed by NM, 19-Feb-2005.)  (New usage is discouraged.) $)
+  $( Two equivalent expressions for double existential uniqueness.  Usage of
+     this theorem is discouraged because it depends on ~ ax-13 .  (Contributed
+     by NM, 19-Feb-2005.)  (New usage is discouraged.) $)
   2eu7 $p |- ( ( E! x E. y ph /\ E! y E. x ph ) <->
              E! x E! y ( E. x ph /\ E. y ph ) ) $=
     ( wex weu wa nfe1 nfeu euan ancom eubii 3bitri 3bitr4ri ) ABDZCEZACDZFZBEOP
@@ -24206,7 +24412,8 @@ correct definition apparently has never been published ( ` E* ` means
 
   $( Two equivalent expressions for double existential uniqueness.  Curiously,
      we can put ` E! ` on either of the internal conjuncts but not both.  We
-     can also commute ` E! x E! y ` using ~ 2eu7 .  (Contributed by NM,
+     can also commute ` E! x E! y ` using ~ 2eu7 .  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  (Contributed by NM,
      20-Feb-2005.)  (New usage is discouraged.) $)
   2eu8 $p |- ( E! x E! y ( E. x ph /\ E. y ph ) <->
                 E! x E! y ( E! x ph /\ E. y ph ) ) $=
@@ -24943,9 +25150,10 @@ number of additional axioms (mainly to replace definitions like ~ df-or and
   $( Axiom of Quantifier Introduction (intuitionistic logic axiom ax-i12).  In
      classical logic, this is mostly a restatement of ~ axc9 (with one
      additional quantifier).  But in intuitionistic logic, changing the
-     negations and implications to disjunctions makes it stronger.
-     (Contributed by Jim Kingdon, 31-Dec-2017.)  Avoid ~ ax-11 .  (Revised by
-     Wolf Lammen, 24-Apr-2023.)  (New usage is discouraged.) $)
+     negations and implications to disjunctions makes it stronger.  Usage of
+     this theorem is discouraged because it depends on ~ ax-13 .  (Contributed
+     by Jim Kingdon, 31-Dec-2017.)  Avoid ~ ax-11 .  (Revised by Wolf Lammen,
+     24-Apr-2023.)  (New usage is discouraged.) $)
   axi12 $p |- ( A. z z = x \/ ( A. z z = y \/
                 A. z ( x = y -> A. z x = y ) ) ) $=
     ( weq wal wo wi nfa1 nfor 19.32 wn axc9 orrd orri orass mpbir mpgbi mpbi )
@@ -24964,9 +25172,10 @@ number of additional axioms (mainly to replace definitions like ~ df-or and
   $( Axiom of Bundling (intuitionistic logic axiom ax-bnd).  In classical
      logic, this and ~ axi12 are fairly straightforward consequences of
      ~ axc9 .  But in intuitionistic logic, it is not easy to add the extra
-     ` A. x ` to ~ axi12 and so we treat the two as separate axioms.
-     (Contributed by Jim Kingdon, 22-Mar-2018.)  (Proof shortened by Wolf
-     Lammen, 24-Apr-2023.)  (New usage is discouraged.) $)
+     ` A. x ` to ~ axi12 and so we treat the two as separate axioms.  Usage of
+     this theorem is discouraged because it depends on ~ ax-13 .  (Contributed
+     by Jim Kingdon, 22-Mar-2018.)  (Proof shortened by Wolf Lammen,
+     24-Apr-2023.)  (New usage is discouraged.) $)
   axbnd $p |- ( A. z z = x \/ ( A. z z = y \/
                  A. x A. z ( x = y -> A. z x = y ) ) ) $=
     ( weq wal wo wi nfae nfor 19.32 orass bitri axi12 mpbir mpgbi ) CADCEZCBDCE
@@ -25355,7 +25564,8 @@ yield an eliminable and weakly (that is, object-level) conservative
   ${
     $d x z $.
     hbabg.1 $e |- ( ph -> A. x ph ) $.
-    $( Bound-variable hypothesis builder for a class abstraction.  See ~ hbab
+    $( Bound-variable hypothesis builder for a class abstraction.  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .  See ~ hbab
        for a version with more disjoint variable conditions, but not requiring
        ~ ax-13 .  (Contributed by NM, 1-Mar-1995.)
        (New usage is discouraged.) $)
@@ -25378,7 +25588,8 @@ yield an eliminable and weakly (that is, object-level) conservative
   ${
     $d x z $.
     nfsabg.1 $e |- F/ x ph $.
-    $( Bound-variable hypothesis builder for a class abstraction.  See ~ nfsab
+    $( Bound-variable hypothesis builder for a class abstraction.  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .  See ~ nfsab
        for a version with more disjoint variable conditions, but not requiring
        ~ ax-13 .  (Contributed by Mario Carneiro, 11-Aug-2016.)
        (New usage is discouraged.) $)
@@ -26385,9 +26596,11 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     cbvab.1 $e |- F/ y ph $.
     cbvab.2 $e |- F/ x ps $.
     cbvab.3 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by Andrew Salmon, 11-Jul-2011.)  (Proof shortened by Wolf
-       Lammen, 16-Nov-2019.)  (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Usage of
+       the weaker ~ cbvabw and ~ cbvabv are preferred.  (Contributed by Andrew
+       Salmon, 11-Jul-2011.)  (Proof shortened by Wolf Lammen, 16-Nov-2019.)
+       (New usage is discouraged.) $)
     cbvab $p |- { x | ph } = { y | ps } $=
       ( vz cab wsb cv wcel sbco2 sbie sbbii bitr3i df-clab 3bitr4i eqriv ) HACI
       ZBDIZACHJZBDHJZHKZTLUDUALUBACDJZDHJUCACHDEMUEBDHABCDFGNOPAHCQBHDQRS $.
@@ -26909,7 +27122,8 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
   ${
     $d y A $.  $d x z $.
     hblemg.1 $e |- ( y e. A -> A. x y e. A ) $.
-    $( Change the free variable of a hypothesis builder.  See ~ hblem for a
+    $( Change the free variable of a hypothesis builder.  Usage of this theorem
+       is discouraged because it depends on ~ ax-13 .  See ~ hblem for a
        version with more disjoint variable conditions, but not requiring
        ~ ax-13 .  (Contributed by NM, 21-Jun-1993.)  (Revised by Andrew Salmon,
        11-Jul-2011.)  (New usage is discouraged.) $)
@@ -27318,8 +27532,9 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
   ${
     $d w x $.  $d w A $.  $d w y $.
     clelsb3f.1 $e |- F/_ x A $.
-    $( Substitution applied to an atomic wff (class version of ~ elsb3 ).  See
-       ~ clelsb3fw not requiring ~ ax-13 , but extra disjoint variables.
+    $( Substitution applied to an atomic wff (class version of ~ elsb3 ).
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       See ~ clelsb3fw not requiring ~ ax-13 , but extra disjoint variables.
        (Contributed by Rodolfo Medina, 28-Apr-2010.)  (Proof shortened by
        Andrew Salmon, 14-Jun-2011.)  (Revised by Thierry Arnoux, 13-Mar-2017.)
        (Proof shortened by Wolf Lammen, 7-May-2023.)
@@ -27352,7 +27567,8 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
   ${
     $d x z $.  $d y z $.  $d z ph $.
     nfabg.1 $e |- F/ x ph $.
-    $( Bound-variable hypothesis builder for a class abstraction.  See ~ nfab
+    $( Bound-variable hypothesis builder for a class abstraction.  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .  See ~ nfab
        for a version with more disjoint variable conditions, but not requiring
        ~ ax-13 .  (Contributed by Mario Carneiro, 11-Aug-2016.)
        (New usage is discouraged.) $)
@@ -27371,9 +27587,10 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     $( $j usage 'nfaba1' avoids 'ax-13'; $)
   $}
 
-  $( Bound-variable hypothesis builder for a class abstraction.  See ~ nfaba1
-     for a version with disjoint variable conditions, but not requiring
-     ~ ax-13 .  (Contributed by Mario Carneiro, 14-Oct-2016.)
+  $( Bound-variable hypothesis builder for a class abstraction.  Usage of this
+     theorem is discouraged because it depends on ~ ax-13 .  See ~ nfaba1 for a
+     version with a disjoint variable condition, but not requiring ~ ax-13 .
+     (Contributed by Mario Carneiro, 14-Oct-2016.)
      (New usage is discouraged.) $)
   nfaba1g $p |- F/_ x { y | A. x ph } $=
     ( wal nfa1 nfabg ) ABDBCABEF $.
@@ -27452,6 +27669,7 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     $d w x $.  $d w y $.  $d w z $.  $d w A $.  $d w B $.
     drnfc1.1 $e |- ( A. x x = y -> A = B ) $.
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by Mario Carneiro, 8-Oct-2016.)  Avoid ~ ax-11 .  (Revised
        by Wolf Lammen, 10-May-2023.)  (New usage is discouraged.) $)
     drnfc1 $p |- ( A. x x = y -> ( F/_ x A <-> F/_ y B ) ) $=
@@ -27469,7 +27687,8 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     $( Formula-building lemma for use with the Distinctor Reduction Theorem.
        Proof revision is marked as discouraged because the minimizer replaces
        ~ albidv with ~ dral2 , leading to a one byte longer proof.  However
-       feel free to manually edit it according to conventions.  (Contributed by
+       feel free to manually edit it according to conventions.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
        Mario Carneiro, 8-Oct-2016.)  (Proof modification is discouraged.)
        (New usage is discouraged.) $)
     drnfc2 $p |- ( A. x x = y -> ( F/_ z A <-> F/_ z B ) ) $=
@@ -27497,9 +27716,11 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     $d x z $.  $d y z $.  $d z ph $.  $d z ps $.
     nfabd.1 $e |- F/ y ph $.
     nfabd.2 $e |- ( ph -> F/ x ps ) $.
-    $( Bound-variable hypothesis builder for a class abstraction.  (Contributed
-       by Mario Carneiro, 8-Oct-2016.)  Avoid ~ ax-9 and ~ ax-ext .  (Revised
-       by Wolf Lammen, 23-May-2023.)  (New usage is discouraged.) $)
+    $( Bound-variable hypothesis builder for a class abstraction.  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ nfabdw when possible.  (Contributed by Mario Carneiro,
+       8-Oct-2016.)  Avoid ~ ax-9 and ~ ax-ext .  (Revised by Wolf Lammen,
+       23-May-2023.)  (New usage is discouraged.) $)
     nfabd $p |- ( ph -> F/_ x { y | ps } ) $=
       ( vz cab nfv cv wcel wsb df-clab nfsbd nfxfrd nfcd ) ACGBDHZAGIGJQKBDGLAC
       BGDMABDGCEFNOP $.
@@ -27509,9 +27730,10 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
   ${
     nfabd2.1 $e |- F/ y ph $.
     nfabd2.2 $e |- ( ( ph /\ -. A. x x = y ) -> F/ x ps ) $.
-    $( Bound-variable hypothesis builder for a class abstraction.  (Contributed
-       by Mario Carneiro, 8-Oct-2016.)  (Proof shortened by Wolf Lammen,
-       10-May-2023.)  (New usage is discouraged.) $)
+    $( Bound-variable hypothesis builder for a class abstraction.  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .
+       (Contributed by Mario Carneiro, 8-Oct-2016.)  (Proof shortened by Wolf
+       Lammen, 10-May-2023.)  (New usage is discouraged.) $)
     nfabd2 $p |- ( ph -> F/_ x { y | ps } ) $=
       ( weq wal cab wnfc wn wa nfnae nfan nfabd ex nfab1 eqidd drnfc1 mpbiri
       pm2.61d2 ) ACDGCHZCBDIZJZAUBKZUDAUELBCDAUEDECDDMNFOPUBUDDUCJBDQCDUCUCUBUC
@@ -27545,7 +27767,8 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     dvelimdc.3 $e |- ( ph -> F/_ x A ) $.
     dvelimdc.4 $e |- ( ph -> F/_ z B ) $.
     dvelimdc.5 $e |- ( ph -> ( z = y -> A = B ) ) $.
-    $( Deduction form of ~ dvelimc .  (Contributed by Mario Carneiro,
+    $( Deduction form of ~ dvelimc .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by Mario Carneiro,
        8-Oct-2016.)  (New usage is discouraged.) $)
     dvelimdc $p |- ( ph -> ( -. A. x x = y -> F/_ x B ) ) $=
       ( vw weq wal wn wnfc wa nfv wcel nfcrd cv wnf wceq wb eleq2 syl6 dvelimdf
@@ -27557,7 +27780,8 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
     dvelimc.1 $e |- F/_ x A $.
     dvelimc.2 $e |- F/_ z B $.
     dvelimc.3 $e |- ( z = y -> A = B ) $.
-    $( Version of ~ dvelim for classes.  (Contributed by Mario Carneiro,
+    $( Version of ~ dvelim for classes.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by Mario Carneiro,
        8-Oct-2016.)  (New usage is discouraged.) $)
     dvelimc $p |- ( -. A. x x = y -> F/_ x B ) $=
       ( weq wal wn wnfc wi wtru nftru a1i wceq dvelimdc mptru ) ABIAJKAELMNABCD
@@ -27567,16 +27791,21 @@ the definition of class equality ( ~ df-cleq ).  Its forward implication
   ${
     $d x w z $.  $d y w z $.
     $( If ` x ` and ` y ` are distinct, then ` x ` is not free in ` y ` .
-       (Contributed by Mario Carneiro, 8-Oct-2016.)  Avoid ~ ax-ext .  (Revised
-       by Wolf Lammen, 10-May-2023.)  (New usage is discouraged.) $)
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       See ~ nfcv for a version that replaces the distinctor with a disjoint
+       variable condition, requiring fewer axioms.  (Contributed by Mario
+       Carneiro, 8-Oct-2016.)  Avoid ~ ax-ext .  (Revised by Wolf Lammen,
+       10-May-2023.)  (New usage is discouraged.) $)
     nfcvf $p |- ( -. A. x x = y -> F/_ x y ) $=
       ( vw vz weq wal wn cv nfv wel elequ2 dvelimnf nfcd ) ABEAFGZACBHNCICDJZCB
       JABDOAIDBCKLM $.
     $( $j usage 'nfcvf' avoids 'ax-ext'; $)
 
     $( If ` x ` and ` y ` are distinct, then ` y ` is not free in ` x ` .
-       (Contributed by Mario Carneiro, 5-Dec-2016.)
-       (New usage is discouraged.) $)
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       See ~ nfcv for a version that replaces the distinctor with a disjoint
+       variable condition, requiring fewer axioms.  (Contributed by Mario
+       Carneiro, 5-Dec-2016.)  (New usage is discouraged.) $)
     nfcvf2 $p |- ( -. A. x x = y -> F/_ y x ) $=
       ( cv wnfc nfcvf naecoms ) BACDBABAEF $.
   $}
@@ -29185,9 +29414,12 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     $d x y $.  $d y A $.
     rgen2.1 $e |- ( ( x e. A /\ y e. B ) -> ph ) $.
     $( Generalization rule for restricted quantification, with two quantifiers.
-       (Contributed by NM, 30-May-1999.) $)
+       This theorem should be used in place of ~ rgen2a since it depends on a
+       smaller set of axioms.  (Contributed by NM, 30-May-1999.) $)
     rgen2 $p |- A. x e. A A. y e. B ph $=
       ( wral cv wcel ralrimiva rgen ) ACEGBDBHDIACEFJK $.
+    $( $j usage 'rgen2' avoids 'ax-6' 'ax-7' 'ax-8' 'ax-9' 'ax-10' 'ax-11'
+       'ax-12' 'ax-13' 'ax-ext'; $)
   $}
 
   ${
@@ -29360,8 +29592,10 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     nfrald.1 $e |- F/ y ph $.
     nfrald.2 $e |- ( ph -> F/_ x A ) $.
     nfrald.3 $e |- ( ph -> F/ x ps ) $.
-    $( Deduction version of ~ nfral .  (Contributed by NM, 15-Feb-2013.)
-       (Revised by Mario Carneiro, 7-Oct-2016.)  (New usage is discouraged.) $)
+    $( Deduction version of ~ nfral .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ nfraldw when possible.
+       (Contributed by NM, 15-Feb-2013.)  (Revised by Mario Carneiro,
+       7-Oct-2016.)  (New usage is discouraged.) $)
     nfrald $p |- ( ph -> F/ x A. y e. A ps ) $=
       ( wral cv wcel wi wal df-ral weq wn wa wnfc nfcvf adantr adantl nfeld wnf
       nfimd nfald2 nfxfrd ) BDEIDJZEKZBLZDMACBDENAUICDFACDOCMPZQZUHBCUKCUGEUJCU
@@ -29383,9 +29617,10 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
   ${
     nfral.1 $e |- F/_ x A $.
     nfral.2 $e |- F/ x ph $.
-    $( Bound-variable hypothesis builder for restricted quantification.
-       (Contributed by NM, 1-Sep-1999.)  (Revised by Mario Carneiro,
-       7-Oct-2016.)  (New usage is discouraged.) $)
+    $( Bound-variable hypothesis builder for restricted quantification.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ nfralw when possible.  (Contributed by NM, 1-Sep-1999.)
+       (Revised by Mario Carneiro, 7-Oct-2016.)  (New usage is discouraged.) $)
     nfral $p |- F/ x A. y e. A ph $=
       ( wral wnf wtru nftru wnfc a1i nfrald mptru ) ACDGBHIABCDCJBDKIELABHIFLMN
       $.
@@ -29404,7 +29639,9 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     $d A y $.
     $( Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the
        antecedent is restricted.  Derived automatically from ~ hbra2VD .
-       Contributed by Alan Sare 31-Dec-2011.  (Contributed by NM, 31-Dec-2011.)
+       Contributed by Alan Sare 31-Dec-2011.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ nfra2w
+       when possible.  (Contributed by NM, 31-Dec-2011.)
        (New usage is discouraged.) $)
     nfra2 $p |- F/ y A. x e. A A. y e. B ph $=
       ( wral nfcv nfra1 nfral ) ACEFCBDCDGACEHI $.
@@ -29415,7 +29652,9 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     rgen2a.1 $e |- ( ( x e. A /\ y e. A ) -> ph ) $.
     $( Generalization rule for restricted quantification.  Note that ` x ` and
        ` y ` are not required to be disjoint.  This proof illustrates the use
-       of ~ dvelim .  (Contributed by NM, 23-Nov-1994.)  (Proof shortened by
+       of ~ dvelim .  This theorem relies on the full set of axioms up to
+       ~ ax-ext and it should no longer be used.  Usage of ~ rgen2 is highly
+       encouraged.  (Contributed by NM, 23-Nov-1994.)  (Proof shortened by
        Andrew Salmon, 25-May-2011.)  (Proof shortened by Wolf Lammen,
        1-Jan-2020.)  (Proof modification is discouraged.)
        (New usage is discouraged.) $)
@@ -30115,8 +30354,9 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     nfrexdg.1 $e |- F/ y ph $.
     nfrexdg.2 $e |- ( ph -> F/_ x A ) $.
     nfrexdg.3 $e |- ( ph -> F/ x ps ) $.
-    $( Deduction version of ~ nfrexg .  See ~ nfrexd for a version with
-       disjoint variable conditions, but not requiring ~ ax-13 .  (Contributed
+    $( Deduction version of ~ nfrexg .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  See ~ nfrexd for a version with a
+       disjoint variable condition, but not requiring ~ ax-13 .  (Contributed
        by Mario Carneiro, 14-Oct-2016.)  (New usage is discouraged.) $)
     nfrexdg $p |- ( ph -> F/ x E. y e. A ps ) $=
       ( wrex wn wral dfrex2 nfnd nfrald nfxfrd ) BDEIBJZDEKZJACBDELAQCAPCDEFGAB
@@ -30142,8 +30382,9 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
   ${
     nfrexg.1 $e |- F/_ x A $.
     nfrexg.2 $e |- F/ x ph $.
-    $( Bound-variable hypothesis builder for restricted quantification.  See
-       ~ nfrex for a version with disjoint variable conditions, but not
+    $( Bound-variable hypothesis builder for restricted quantification.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  See
+       ~ nfrex for a version with a disjoint variable condition, but not
        requiring ~ ax-13 .  (Contributed by NM, 1-Sep-1999.)  (Revised by Mario
        Carneiro, 7-Oct-2016.)  (Proof shortened by Wolf Lammen, 30-Dec-2019.)
        (New usage is discouraged.) $)
@@ -30668,8 +30909,10 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     $d y A $.  $d x A $.
     $( Commutation of restricted universal quantifiers.  Note that ` x ` and
        ` y ` need not be disjoint (this makes the proof longer).  If ` x ` and
-       ` y ` are disjoint, then one may use ~ ralcom .  (Contributed by NM,
-       24-Nov-1994.)  (Proof shortened by Mario Carneiro, 17-Oct-2016.)
+       ` y ` are disjoint, then one may use ~ ralcom .  Usage of this theorem
+       is discouraged because it depends on ~ ax-13 .  Use the weaker
+       ~ ralcom2w when possible.  (Contributed by NM, 24-Nov-1994.)  (Proof
+       shortened by Mario Carneiro, 17-Oct-2016.)
        (New usage is discouraged.) $)
     ralcom2 $p |- ( A. x e. A A. y e. A ph -> A. y e. A A. x e. A ph ) $=
       ( weq wal wral wi cv wcel wb eleq1w dral1 df-ral 3bitr4g wa nfnae ralrimi
@@ -30762,14 +31005,16 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     nfreud.1 $e |- F/ y ph $.
     nfreud.2 $e |- ( ph -> F/_ x A ) $.
     nfreud.3 $e |- ( ph -> F/ x ps ) $.
-    $( Deduction version of ~ nfreu .  (Contributed by NM, 15-Feb-2013.)
+    $( Deduction version of ~ nfreu .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by NM, 15-Feb-2013.)
        (Revised by Mario Carneiro, 8-Oct-2016.)  (New usage is discouraged.) $)
     nfreud $p |- ( ph -> F/ x E! y e. A ps ) $=
       ( wreu cv wcel wa weu df-reu weq wal wn wnfc nfcvf adantr nfeld wnf nfand
       adantl nfeud2 nfxfrd ) BDEIDJZEKZBLZDMACBDENAUICDFACDOCPQZLZUHBCUKCUGEUJC
       UGRACDSUDACERUJGTUAABCUBUJHTUCUEUF $.
 
-    $( Deduction version of ~ nfrmo .  (Contributed by NM, 17-Jun-2017.)
+    $( Deduction version of ~ nfrmo .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by NM, 17-Jun-2017.)
        (New usage is discouraged.) $)
     nfrmod $p |- ( ph -> F/ x E* y e. A ps ) $=
       ( wrmo cv wcel wa wmo df-rmo weq wal wn wnfc nfcvf adantr nfeld wnf nfand
@@ -30802,14 +31047,18 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     nfreu.1 $e |- F/_ x A $.
     nfreu.2 $e |- F/ x ph $.
     $( Bound-variable hypothesis builder for restricted unique existence.
-       (Contributed by NM, 30-Oct-2010.)  (Revised by Mario Carneiro,
-       8-Oct-2016.)  (New usage is discouraged.) $)
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       Use the weaker ~ nfreuw when possible.  (Contributed by NM,
+       30-Oct-2010.)  (Revised by Mario Carneiro, 8-Oct-2016.)
+       (New usage is discouraged.) $)
     nfreu $p |- F/ x E! y e. A ph $=
       ( wreu wnf wtru nftru wnfc a1i nfreud mptru ) ACDGBHIABCDCJBDKIELABHIFLMN
       $.
 
-    $( Bound-variable hypothesis builder for restricted uniqueness.
-       (Contributed by NM, 16-Jun-2017.)  (New usage is discouraged.) $)
+    $( Bound-variable hypothesis builder for restricted uniqueness.  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ nfrmow when possible.  (Contributed by NM, 16-Jun-2017.)
+       (New usage is discouraged.) $)
     nfrmo $p |- F/ x E* y e. A ph $=
       ( wrmo cv wcel wa wmo df-rmo wnf wtru nftru weq wal wn nfcvf a1i adantl
       wnfc nfeld nfand nfmod2 mptru nfxfr ) ACDGCHZDIZAJZCKZBACDLUKBMNUJBCCOBCP
@@ -30884,8 +31133,10 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     nfrab.1 $e |- F/ x ph $.
     nfrab.2 $e |- F/_ x A $.
     $( A variable not free in a wff remains so in a restricted class
-       abstraction.  (Contributed by NM, 13-Oct-2003.)  (Revised by Mario
-       Carneiro, 9-Oct-2016.)  (New usage is discouraged.) $)
+       abstraction.  Usage of this theorem is discouraged because it depends on
+       ~ ax-13 .  Use the weaker ~ nfrabw when possible.  (Contributed by NM,
+       13-Oct-2003.)  (Revised by Mario Carneiro, 9-Oct-2016.)
+       (New usage is discouraged.) $)
     nfrab $p |- F/_ x { y e. A | ph } $=
       ( vz crab cv wcel wa cab df-rab wnfc wtru nftru weq wal wn wnf eleq1w a1i
       nfcri dvelimnf nfand adantl nfabd2 mptru nfcxfr ) BACDHCIDJZAKZCLZACDMBUL
@@ -31319,9 +31570,10 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     cbvralf.3 $e |- F/ y ph $.
     cbvralf.4 $e |- F/ x ps $.
     cbvralf.5 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 7-Mar-2004.)  (Revised by Mario Carneiro,
-       9-Oct-2016.)  (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ cbvralfw when possible.  (Contributed by NM, 7-Mar-2004.)
+       (Revised by Mario Carneiro, 9-Oct-2016.)  (New usage is discouraged.) $)
     cbvralf $p |- ( A. x e. A ph <-> A. y e. A ps ) $=
       ( vz cv wcel wi wal wral wsb nfv nfcri nfim nfs1v sbequ12 imbi12d cbvalv1
       weq eleq1w nfsb sbequ sbie syl6bb bitri df-ral 3bitr4i ) CLEMZANZCOZDLEMZ
@@ -31329,9 +31581,10 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
       FACKUBUCUDVBURKDUTVADDKEGSACKDHUGTURKRKDUEZUTUQVABKDEUFVCVAACDQBAKDCUHABC
       DIJUIUJUCUDUKACEULBDEULUM $.
 
-    $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by FL, 27-Apr-2008.)  (Revised by Mario Carneiro,
-       9-Oct-2016.)  (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ cbvrexfw when possible.  (Contributed by FL, 27-Apr-2008.)
+       (Revised by Mario Carneiro, 9-Oct-2016.)  (New usage is discouraged.) $)
     cbvrexf $p |- ( E. x e. A ph <-> E. y e. A ps ) $=
       ( wn wral wrex nfn weq notbid cbvralf notbii dfrex2 3bitr4i ) AKZCELZKBKZ
       DELZKACEMBDEMUBUDUAUCCDEFGADHNBCINCDOABJPQRACESBDEST $.
@@ -31389,20 +31642,26 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     cbvral.1 $e |- F/ y ph $.
     cbvral.2 $e |- F/ x ps $.
     cbvral.3 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 31-Jul-2003.)  (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ cbvralw when possible.  (Contributed by NM, 31-Jul-2003.)
+       (New usage is discouraged.) $)
     cbvral $p |- ( A. x e. A ph <-> A. y e. A ps ) $=
       ( nfcv cbvralf ) ABCDECEIDEIFGHJ $.
 
-    $( Rule used to change bound variables, using implicit substitution.
-       (Contributed by NM, 31-Jul-2003.)  (Proof shortened by Andrew Salmon,
-       8-Jun-2011.)  (New usage is discouraged.) $)
+    $( Rule used to change bound variables, using implicit substitution.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ cbvrexw when possible.  (Contributed by NM, 31-Jul-2003.)
+       (Proof shortened by Andrew Salmon, 8-Jun-2011.)
+       (New usage is discouraged.) $)
     cbvrex $p |- ( E. x e. A ph <-> E. y e. A ps ) $=
       ( nfcv cbvrexf ) ABCDECEIDEIFGHJ $.
 
     $( Change the bound variable of a restricted unique existential quantifier
-       using implicit substitution.  (Contributed by Mario Carneiro,
-       15-Oct-2016.)  (New usage is discouraged.) $)
+       using implicit substitution.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ cbvreuw when possible.
+       (Contributed by Mario Carneiro, 15-Oct-2016.)
+       (New usage is discouraged.) $)
     cbvreu $p |- ( E! x e. A ph <-> E! y e. A ps ) $=
       ( vz cv wcel wa weu wreu wsb nfv sb8eu sban eubii df-reu anbi1i nfsb nfan
       clelsb3 weq eleq1w sbequ sbie syl6bb anbi12d cbveu bitri 3bitri 3bitr4i )
@@ -31411,8 +31670,9 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
       VFURVCBIDEUFVHVCACDOBAIDCUGABCDGHUHUIUJUKULUMACETBDETUN $.
 
     $( Change the bound variable of a restricted at-most-one quantifier using
-       implicit substitution.  (Contributed by NM, 16-Jun-2017.)
-       (New usage is discouraged.) $)
+       implicit substitution.  Usage of this theorem is discouraged because it
+       depends on ~ ax-13 .  Use the weaker ~ cbvrmow when possible.
+       (Contributed by NM, 16-Jun-2017.)  (New usage is discouraged.) $)
     cbvrmo $p |- ( E* x e. A ph <-> E* y e. A ps ) $=
       ( wrex wreu wi wrmo cbvrex cbvreu imbi12i rmo5 3bitr4i ) ACEIZACEJZKBDEIZ
       BDEJZKACELBDELRTSUAABCDEFGHMABCDEFGHNOACEPBDEPQ $.
@@ -31449,28 +31709,32 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     cbvralv.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Change the bound variable of a restricted universal quantifier using
        implicit substitution.  See ~ cbvralvw based on fewer axioms , but extra
-       disjoint variables.  (Contributed by NM, 28-Jan-1997.)
-       (New usage is discouraged.) $)
+       disjoint variables.  Usage of this theorem is discouraged because it
+       depends on ~ ax-13 .  Use the weaker ~ cbvralvw when possible.
+       (Contributed by NM, 28-Jan-1997.)  (New usage is discouraged.) $)
     cbvralv $p |- ( A. x e. A ph <-> A. y e. A ps ) $=
       ( nfv cbvral ) ABCDEADGBCGFH $.
 
     $( Change the bound variable of a restricted existential quantifier using
        implicit substitution.  See ~ cbvrexvw based on fewer axioms , but extra
-       disjoint variables.  (Contributed by NM, 2-Jun-1998.)
-       (New usage is discouraged.) $)
+       disjoint variables.  Usage of this theorem is discouraged because it
+       depends on ~ ax-13 .  Use the weaker ~ cbvrexvw when possible.
+       (Contributed by NM, 2-Jun-1998.)  (New usage is discouraged.) $)
     cbvrexv $p |- ( E. x e. A ph <-> E. y e. A ps ) $=
       ( nfv cbvrex ) ABCDEADGBCGFH $.
 
     $( Change the bound variable of a restricted unique existential quantifier
        using implicit substitution.  See ~ cbvreuvw for a version without
-       ~ ax-13 , but extra disjoint variables.  (Contributed by NM,
-       5-Apr-2004.)  (Revised by Mario Carneiro, 15-Oct-2016.)
-       (New usage is discouraged.) $)
+       ~ ax-13 , but extra disjoint variables.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ cbvreuvw
+       when possible.  (Contributed by NM, 5-Apr-2004.)  (Revised by Mario
+       Carneiro, 15-Oct-2016.)  (New usage is discouraged.) $)
     cbvreuv $p |- ( E! x e. A ph <-> E! y e. A ps ) $=
       ( nfv cbvreu ) ABCDEADGBCGFH $.
 
     $( Change the bound variable of a restricted at-most-one quantifier using
-       implicit substitution.  (Contributed by Alexander van der Vekens,
+       implicit substitution.  Usage of this theorem is discouraged because it
+       depends on ~ ax-13 .  (Contributed by Alexander van der Vekens,
        17-Jun-2017.)  (New usage is discouraged.) $)
     cbvrmov $p |- ( E* x e. A ph <-> E* y e. A ps ) $=
       ( nfv cbvrmo ) ABCDEADGBCGFH $.
@@ -31575,7 +31839,9 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     cbvral2v.1 $e |- ( x = z -> ( ph <-> ch ) ) $.
     cbvral2v.2 $e |- ( y = w -> ( ch <-> ps ) ) $.
     $( Change bound variables of double restricted universal quantification,
-       using implicit substitution.  (Contributed by NM, 10-Aug-2004.)
+       using implicit substitution.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ cbvral2vw when
+       possible.  (Contributed by NM, 10-Aug-2004.)
        (New usage is discouraged.) $)
     cbvral2v $p |- ( A. x e. A A. y e. B ph <-> A. z e. A A. w e. B ps ) $=
       ( wral weq ralbidv cbvralv ralbii bitri ) AEILZDHLCEILZFHLBGILZFHLRSDFHDF
@@ -31588,7 +31854,9 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     cbvrex2v.1 $e |- ( x = z -> ( ph <-> ch ) ) $.
     cbvrex2v.2 $e |- ( y = w -> ( ch <-> ps ) ) $.
     $( Change bound variables of double restricted universal quantification,
-       using implicit substitution.  (Contributed by FL, 2-Jul-2012.)
+       using implicit substitution.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ cbvrex2vw when
+       possible.  (Contributed by FL, 2-Jul-2012.)
        (New usage is discouraged.) $)
     cbvrex2v $p |- ( E. x e. A E. y e. B ph <-> E. z e. A E. w e. B ps ) $=
       ( wrex weq rexbidv cbvrexv rexbii bitri ) AEILZDHLCEILZFHLBGILZFHLRSDFHDF
@@ -31603,7 +31871,9 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     cbvral3v.2 $e |- ( y = v -> ( ch <-> th ) ) $.
     cbvral3v.3 $e |- ( z = u -> ( th <-> ps ) ) $.
     $( Change bound variables of triple restricted universal quantification,
-       using implicit substitution.  (Contributed by NM, 10-May-2005.)
+       using implicit substitution.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ cbvral3vw when
+       possible.  (Contributed by NM, 10-May-2005.)
        (New usage is discouraged.) $)
     cbvral3v $p |- ( A. x e. A A. y e. B A. z e. C ph <->
                      A. w e. A A. v e. B A. u e. C ps ) $=
@@ -31633,9 +31903,10 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
 
   ${
     $d z x A $.  $d y A $.  $d z y ph $.
-    $( Change bound variable by using a substitution.  (Contributed by NM,
-       20-Nov-2005.)  (Revised by Andrew Salmon, 11-Jul-2011.)
-       (New usage is discouraged.) $)
+    $( Change bound variable by using a substitution.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ cbvralsvw
+       when possible.  (Contributed by NM, 20-Nov-2005.)  (Revised by Andrew
+       Salmon, 11-Jul-2011.)  (New usage is discouraged.) $)
     cbvralsv $p |- ( A. x e. A ph <-> A. y e. A [ y / x ] ph ) $=
       ( vz wral wsb nfv nfs1v sbequ12 cbvral nfsb sbequ bitri ) ABDFABEGZEDFABC
       GZCDFAOBEDAEHABEIABEJKOPECDABECACHLPEHAECBMKN $.
@@ -31643,9 +31914,10 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
 
   ${
     $d z x A $.  $d y z ph $.  $d y A $.
-    $( Change bound variable by using a substitution.  (Contributed by NM,
-       2-Mar-2008.)  (Revised by Andrew Salmon, 11-Jul-2011.)
-       (New usage is discouraged.) $)
+    $( Change bound variable by using a substitution.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ cbvrexsvw
+       when possible.  (Contributed by NM, 2-Mar-2008.)  (Revised by Andrew
+       Salmon, 11-Jul-2011.)  (New usage is discouraged.) $)
     cbvrexsv $p |- ( E. x e. A ph <-> E. y e. A [ y / x ] ph ) $=
       ( vz wrex wsb nfv nfs1v sbequ12 cbvrex nfsb sbequ bitri ) ABDFABEGZEDFABC
       GZCDFAOBEDAEHABEIABEJKOPECDABECACHLPEHAECBMKN $.
@@ -31846,9 +32118,10 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     cbvrab.5 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Rule to change the bound variable in a restricted class abstraction,
        using implicit substitution.  This version has bound-variable hypotheses
-       in place of distinct variable conditions.  (Contributed by Andrew
-       Salmon, 11-Jul-2011.)  (Revised by Mario Carneiro, 9-Oct-2016.)
-       (New usage is discouraged.) $)
+       in place of distinct variable conditions.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ cbvrabw
+       when possible.  (Contributed by Andrew Salmon, 11-Jul-2011.)  (Revised
+       by Mario Carneiro, 9-Oct-2016.)  (New usage is discouraged.) $)
     cbvrab $p |- { x e. A | ph } = { y e. A | ps } $=
       ( vz cv wcel wa cab crab wsb nfv nfcri nfan nfs1v weq eleq1w sbequ12 nfsb
       anbi12d cbvab sbequ sbie syl6bb eqtri df-rab 3eqtr4i ) CLEMZANZCOZDLEMZBN
@@ -31977,6 +32250,7 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     eqv $p |- ( A = _V <-> A. x x e. A ) $=
       ( cvv wceq cv wcel wb wal dfcleq vex tbt albii bitr4i ) BCDAEZBFZNCFZGZAH
       OAHABCIOQAPOAJKLM $.
+    $( $j usage 'eqv' avoids 'ax-10' 'ax-11' 'ax-12' 'ax-13'; $)
   $}
 
   ${
@@ -34343,8 +34617,10 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     euxfr2.1 $e |- A e. _V $.
     euxfr2.2 $e |- E* y x = A $.
     $( Transfer existential uniqueness from a variable ` x ` to another
-       variable ` y ` contained in expression ` A ` .  (Contributed by NM,
-       14-Nov-2004.)  (New usage is discouraged.) $)
+       variable ` y ` contained in expression ` A ` .  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ euxfr2w
+       when possible.  (Contributed by NM, 14-Nov-2004.)
+       (New usage is discouraged.) $)
     euxfr2 $p |- ( E! x E. y ( x = A /\ ph ) <-> E! y ph ) $=
       ( cv wceq wa wex weu wmo wi 2euswap moani ancom mobii mpbi mpg moeq biidd
       impbii ceqsexv eubii bitri ) BGDHZAIZCJBKZUGBJZCKZACKUHUJUGCLZUHUJMBUGBCN
@@ -34358,8 +34634,10 @@ Such interpretation is rarely needed (see also ~ df-ral ).  (Contributed
     euxfr.2 $e |- E! y x = A $.
     euxfr.3 $e |- ( x = A -> ( ph <-> ps ) ) $.
     $( Transfer existential uniqueness from a variable ` x ` to another
-       variable ` y ` contained in expression ` A ` .  (Contributed by NM,
-       14-Nov-2004.)  (New usage is discouraged.) $)
+       variable ` y ` contained in expression ` A ` .  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ euxfrw
+       when possible.  (Contributed by NM, 14-Nov-2004.)
+       (New usage is discouraged.) $)
     euxfr $p |- ( E! x ph <-> E! y ps ) $=
       ( weu cv wceq wa wex euex ax-mp biantrur 19.41v pm5.32i exbii 3bitr2i
       eubii eumoi euxfr2 bitri ) ACICJEKZBLZDMZCIBDIAUGCAUEDMZALUEALZDMUGUHAUED
@@ -34961,13 +35239,15 @@ something like (wi (wceq (cv vx) (cv vy)) wph) ) into just (wcdeq vx vy
 
     ${
       $d x ps $.  $d y ph $.
-      $( Distribute conditional equality over quantification.  (Contributed by
-         Mario Carneiro, 11-Aug-2016.)  (New usage is discouraged.) $)
+      $( Distribute conditional equality over quantification.  Usage of this
+         theorem is discouraged because it depends on ~ ax-13 .  (Contributed
+         by Mario Carneiro, 11-Aug-2016.)  (New usage is discouraged.) $)
       cdeqal1 $p |- CondEq ( x = y -> ( A. x ph <-> A. y ps ) ) $=
         ( wal wb cdeqri cbvalv cdeqth ) ACFBDFGCDABCDABGCDEHIJ $.
 
-      $( Distribute conditional equality over abstraction.  (Contributed by
-         Mario Carneiro, 11-Aug-2016.)  (New usage is discouraged.) $)
+      $( Distribute conditional equality over abstraction.  Usage of this
+         theorem is discouraged because it depends on ~ ax-13 .  (Contributed
+         by Mario Carneiro, 11-Aug-2016.)  (New usage is discouraged.) $)
       cdeqab1 $p |- CondEq ( x = y -> { x | ph } = { y | ps } ) $=
         ( cab wceq nfv wb cdeqri cbvab cdeqth ) ACFBDFGCDABCDADHBCHABICDEJKL $.
     $}
@@ -35007,7 +35287,8 @@ something like (wi (wceq (cv vx) (cv vy)) wph) ) into just (wcdeq vx vy
        and ` ps ` is ` ph ( y ) ` , and ` ph ( x ) ` in fact does not have
        ` x ` free in it according to ` F/ ` , then ` ph ( x ) <-> ph ( y ) `
        unconditionally.  This proves that ` F/ x ph ` is actually a not-free
-       predicate.  (Contributed by Mario Carneiro, 11-Aug-2016.)
+       predicate.  Usage of this theorem is discouraged because it depends on
+       ~ ax-13 .  (Contributed by Mario Carneiro, 11-Aug-2016.)
        (New usage is discouraged.) $)
     nfcdeq $p |- ( ph <-> ps ) $=
       ( wsb sbf nfv wb cdeqri sbie bitr3i ) AACDGBACDEHABCDBCIABJCDFKLM $.
@@ -35017,7 +35298,8 @@ something like (wi (wceq (cv vx) (cv vy)) wph) ) into just (wcdeq vx vy
     $d x z B $.  $d y z A $.
     nfccdeq.1 $e |- F/_ x A $.
     nfccdeq.2 $e |- CondEq ( x = y -> A = B ) $.
-    $( Variation of ~ nfcdeq for classes.  (Contributed by Mario Carneiro,
+    $( Variation of ~ nfcdeq for classes.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by Mario Carneiro,
        11-Aug-2016.)  Avoid ~ ax-11 .  (Revised by Gino Giotto, 19-May-2023.)
        (New usage is discouraged.) $)
     nfccdeq $p |- A = B $=
@@ -35404,9 +35686,10 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     nfsbcd.1 $e |- F/ y ph $.
     nfsbcd.2 $e |- ( ph -> F/_ x A ) $.
     nfsbcd.3 $e |- ( ph -> F/ x ps ) $.
-    $( Deduction version of ~ nfsbc .  (Contributed by NM, 23-Nov-2005.)
-       (Revised by Mario Carneiro, 12-Oct-2016.)
-       (New usage is discouraged.) $)
+    $( Deduction version of ~ nfsbc .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ nfsbcdw when possible.
+       (Contributed by NM, 23-Nov-2005.)  (Revised by Mario Carneiro,
+       12-Oct-2016.)  (New usage is discouraged.) $)
     nfsbcd $p |- ( ph -> F/ x [. A / y ]. ps ) $=
       ( wsbc cab wcel df-sbc nfabd nfeld nfxfrd ) BDEIEBDJZKACBDELACEPGABCDFHMN
       O $.
@@ -35415,9 +35698,10 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
   ${
     nfsbc.1 $e |- F/_ x A $.
     nfsbc.2 $e |- F/ x ph $.
-    $( Bound-variable hypothesis builder for class substitution.  (Contributed
-       by NM, 7-Sep-2014.)  (Revised by Mario Carneiro, 12-Oct-2016.)
-       (New usage is discouraged.) $)
+    $( Bound-variable hypothesis builder for class substitution.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  Use the weaker
+       ~ nfsbcw when possible.  (Contributed by NM, 7-Sep-2014.)  (Revised by
+       Mario Carneiro, 12-Oct-2016.)  (New usage is discouraged.) $)
     nfsbc $p |- F/ x [. A / y ]. ph $=
       ( wsbc wnf wtru nftru wnfc a1i nfsbcd mptru ) ACDGBHIABCDCJBDKIELABHIFLMN
       $.
@@ -35425,9 +35709,10 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
 
   ${
     $d x z $.  $d z A $.  $d y z ph $.
-    $( A composition law for class substitution.  (Contributed by NM,
-       26-Sep-2003.)  (Revised by Mario Carneiro, 13-Oct-2016.)
-       (New usage is discouraged.) $)
+    $( A composition law for class substitution.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ sbccow
+       when possible.  (Contributed by NM, 26-Sep-2003.)  (Revised by Mario
+       Carneiro, 13-Oct-2016.)  (New usage is discouraged.) $)
     sbcco $p |- ( [. A / y ]. [. y / x ]. ph <-> [. A / x ]. ph ) $=
       ( vz cv wsbc cvv wcel sbcex dfsbcq wsb sbsbc sbbii sbco2 3bitr3ri vtoclbg
       nfv bitri pm5.21nii ) ABCFGZCDGZDHIABDGZUACDJABDJUACEFZGZABUDGZUBUCEDHUAC
@@ -35512,9 +35797,10 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     cbvsbc.1 $e |- F/ y ph $.
     cbvsbc.2 $e |- F/ x ps $.
     cbvsbc.3 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( Change bound variables in a wff substitution.  (Contributed by Jeff
-       Hankins, 19-Sep-2009.)  (Proof shortened by Andrew Salmon, 8-Jun-2011.)
-       (New usage is discouraged.) $)
+    $( Change bound variables in a wff substitution.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ cbvsbcw
+       when possible.  (Contributed by Jeff Hankins, 19-Sep-2009.)  (Proof
+       shortened by Andrew Salmon, 8-Jun-2011.)  (New usage is discouraged.) $)
     cbvsbc $p |- ( [. A / x ]. ph <-> [. A / y ]. ps ) $=
       ( cab wcel wsbc cbvab eleq2i df-sbc 3bitr4i ) EACIZJEBDIZJACEKBDEKPQEABCD
       FGHLMACENBDENO $.
@@ -35524,8 +35810,10 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     $d y ph $.  $d x ps $.
     cbvsbcv.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( Change the bound variable of a class substitution using implicit
-       substitution.  (Contributed by NM, 30-Sep-2008.)  (Revised by Mario
-       Carneiro, 13-Oct-2016.)  (New usage is discouraged.) $)
+       substitution.  Usage of this theorem is discouraged because it depends
+       on ~ ax-13 .  Use the weaker ~ cbvsbcvw when possible.  (Contributed by
+       NM, 30-Sep-2008.)  (Revised by Mario Carneiro, 13-Oct-2016.)
+       (New usage is discouraged.) $)
     cbvsbcv $p |- ( [. A / x ]. ph <-> [. A / y ]. ps ) $=
       ( nfv cbvsbc ) ABCDEADGBCGFH $.
   $}
@@ -36405,9 +36693,11 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     cbvcsb.2 $e |- F/_ x D $.
     cbvcsb.3 $e |- ( x = y -> C = D ) $.
     $( Change bound variables in a class substitution.  Interestingly, this
-       does not require any bound variable conditions on ` A ` .  (Contributed
-       by Jeff Hankins, 13-Sep-2009.)  (Revised by Mario Carneiro,
-       11-Dec-2016.)  (New usage is discouraged.) $)
+       does not require any bound variable conditions on ` A ` .  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  Use the weaker
+       ~ cbvcsbw when possible.  (Contributed by Jeff Hankins, 13-Sep-2009.)
+       (Revised by Mario Carneiro, 11-Dec-2016.)
+       (New usage is discouraged.) $)
     cbvcsb $p |- [_ A / x ]_ C = [_ A / y ]_ D $=
       ( vz cv wcel wsbc cab csb nfcri weq eleq2d cbvsbc abbii df-csb 3eqtr4i )
       IJZDKZACLZIMUBEKZBCLZIMACDNBCENUDUFIUCUEABCBIDFOAIEGOABPDEUBHQRSAICDTBICE
@@ -36451,8 +36741,10 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
 
   ${
     $d z A $.  $d y z B $.  $d x z $.
-    $( Composition law for chained substitutions into a class.  (Contributed by
-       NM, 10-Nov-2005.)  (New usage is discouraged.) $)
+    $( Composition law for chained substitutions into a class.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  Use the weaker
+       ~ csbcow when possible.  (Contributed by NM, 10-Nov-2005.)
+       (New usage is discouraged.) $)
     csbco $p |- [_ A / y ]_ [_ y / x ]_ B = [_ A / x ]_ B $=
       ( vz cv csb wcel wsbc cab df-csb abeq2i sbcbii sbcco bitri abbii 3eqtr4i
       ) EFZABFZDGZHZBCIZEJRDHZACIZEJBCTGACDGUBUDEUBUCASIZBCIUDUAUEBCUEETAESDKLM
@@ -36539,7 +36831,8 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     nfcsbd.1 $e |- F/ y ph $.
     nfcsbd.2 $e |- ( ph -> F/_ x A ) $.
     nfcsbd.3 $e |- ( ph -> F/_ x B ) $.
-    $( Deduction version of ~ nfcsb .  (Contributed by NM, 21-Nov-2005.)
+    $( Deduction version of ~ nfcsb .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by NM, 21-Nov-2005.)
        (Revised by Mario Carneiro, 12-Oct-2016.)
        (New usage is discouraged.) $)
     nfcsbd $p |- ( ph -> F/_ x [_ A / y ]_ B ) $=
@@ -36563,9 +36856,10 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
   ${
     nfcsb.1 $e |- F/_ x A $.
     nfcsb.2 $e |- F/_ x B $.
-    $( Bound-variable hypothesis builder for substitution into a class.
-       (Contributed by Mario Carneiro, 12-Oct-2016.)
-       (New usage is discouraged.) $)
+    $( Bound-variable hypothesis builder for substitution into a class.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ nfcsbw when possible.  (Contributed by Mario Carneiro,
+       12-Oct-2016.)  (New usage is discouraged.) $)
     nfcsb $p |- F/_ x [_ A / y ]_ B $=
       ( csb wnfc wtru nftru a1i nfcsbd mptru ) ABCDGHIABCDBJACHIEKADHIFKLM $.
   $}
@@ -36759,7 +37053,8 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     cbvralcsf.6 $e |- ( x = y -> ( ph <-> ps ) ) $.
     $( A more general version of ~ cbvralf that doesn't require ` A ` and ` B `
        to be distinct from ` x ` or ` y ` .  Changes bound variables using
-       implicit substitution.  (Contributed by Andrew Salmon, 13-Jul-2011.)
+       implicit substitution.  Usage of this theorem is discouraged because it
+       depends on ~ ax-13 .  (Contributed by Andrew Salmon, 13-Jul-2011.)
        (New usage is discouraged.) $)
     cbvralcsf $p |- ( A. x e. A ph <-> A. y e. B ps ) $=
       ( vz vv cv wcel wi wal wsbc nfcri wral csb nfv nfcsb1v nfsbc1v id csbeq1a
@@ -36774,6 +37069,7 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
 
     $( A more general version of ~ cbvrexf that has no distinct variable
        restrictions.  Changes bound variables using implicit substitution.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by Andrew Salmon, 13-Jul-2011.)  (Proof shortened by Mario
        Carneiro, 7-Dec-2014.)  (New usage is discouraged.) $)
     cbvrexcsf $p |- ( E. x e. A ph <-> E. y e. B ps ) $=
@@ -36782,6 +37078,7 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
 
     $( A more general version of ~ cbvreuv that has no distinct variable
        restrictions.  Changes bound variables using implicit substitution.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by Andrew Salmon, 13-Jul-2011.)
        (New usage is discouraged.) $)
     cbvreucsf $p |- ( E! x e. A ph <-> E! y e. B ps ) $=
@@ -36796,8 +37093,9 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
       EVLBDFVLVM $.
 
     $( A more general version of ~ cbvrab with no distinct variable
-       restrictions.  (Contributed by Andrew Salmon, 13-Jul-2011.)
-       (New usage is discouraged.) $)
+       restrictions.  Usage of this theorem is discouraged because it depends
+       on ~ ax-13 .  Use the weaker ~ cbvrabcsfw when possible.  (Contributed
+       by Andrew Salmon, 13-Jul-2011.)  (New usage is discouraged.) $)
     cbvrabcsf $p |- { x e. A | ph } = { y e. B | ps } $=
       ( vz vv cv wcel wa cab wsb nfcri crab csb nfv nfcsb1v nfan weq id csbeq1a
       nfs1v eleq12d sbequ12 anbi12d cbvab nfcv nfcsb csbeq1 df-csb eleq2d sbsbc
@@ -36815,14 +37113,16 @@ practical reasons (to avoid having to prove sethood of ` A ` in every use
     cbvralv2.2 $e |- ( x = y -> A = B ) $.
     $( Rule used to change the bound variable in a restricted universal
        quantifier with implicit substitution which also changes the quantifier
-       domain.  (Contributed by David Moews, 1-May-2017.)
+       domain.  Usage of this theorem is discouraged because it depends on
+       ~ ax-13 .  (Contributed by David Moews, 1-May-2017.)
        (New usage is discouraged.) $)
     cbvralv2 $p |- ( A. x e. A ps <-> A. y e. B ch ) $=
       ( nfcv nfv cbvralcsf ) ABCDEFDEICFIADJBCJHGK $.
 
     $( Rule used to change the bound variable in a restricted existential
        quantifier with implicit substitution which also changes the quantifier
-       domain.  (Contributed by David Moews, 1-May-2017.)
+       domain.  Usage of this theorem is discouraged because it depends on
+       ~ ax-13 .  (Contributed by David Moews, 1-May-2017.)
        (New usage is discouraged.) $)
     cbvrexv2 $p |- ( E. x e. A ps <-> E. y e. B ch ) $=
       ( nfcv nfv cbvrexcsf ) ABCDEFDEICFIADJBCJHGK $.
@@ -40367,8 +40667,10 @@ among classes ( ~ eq0 , as opposed to the weaker uniqueness among sets,
 
   ${
     $d x z $.  $d y z $.  $d z A $.  $d z B $.  $d z C $.  $d z ph $.
-    $( Nest the composition of two substitutions.  (Contributed by Mario
-       Carneiro, 11-Nov-2016.)  (New usage is discouraged.) $)
+    $( Nest the composition of two substitutions.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ sbcnestgfw
+       when possible.  (Contributed by Mario Carneiro, 11-Nov-2016.)
+       (New usage is discouraged.) $)
     sbcnestgf $p |- ( ( A e. V /\ A. y F/ x ph ) ->
          ( [. A / x ]. [. B / y ]. ph <-> [. [_ A / x ]_ B / y ]. ph ) ) $=
       ( vz wcel wnf wal wsbc csb wb cv wi wceq dfsbcq sbceq1d cvv a1i vex nfnf1
@@ -40378,9 +40680,10 @@ among classes ( ~ eq0 , as opposed to the weaker uniqueness among sets,
       BNVDPZUSVGMURVJACEVFBVDEUFRUGUQBCABUBUHURABCVFUQCUIBVFUJURBVDEUKTUQCUNULU
       OUMUP $.
 
-    $( Nest the composition of two substitutions.  (Contributed by NM,
-       23-Nov-2005.)  (Proof shortened by Mario Carneiro, 10-Nov-2016.)
-       (New usage is discouraged.) $)
+    $( Nest the composition of two substitutions.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ csbnestgfw
+       when possible.  (Contributed by NM, 23-Nov-2005.)  (Proof shortened by
+       Mario Carneiro, 10-Nov-2016.)  (New usage is discouraged.) $)
     csbnestgf $p |- ( ( A e. V /\ A. y F/_ x C ) ->
          [_ A / x ]_ [_ B / y ]_ C = [_ [_ A / x ]_ B / y ]_ C ) $=
       ( vz wcel wnfc wal wa cv csb wsbc cab cvv wceq elex df-csb abeq2i wb nfcr
@@ -40390,18 +40693,20 @@ among classes ( ~ eq0 , as opposed to the weaker uniqueness among sets,
       FUGUHUIUJAGCUPSBGVAESUK $.
 
     $d x ph $.
-    $( Nest the composition of two substitutions.  (Contributed by NM,
-       27-Nov-2005.)  (Proof shortened by Mario Carneiro, 11-Nov-2016.)
-       (New usage is discouraged.) $)
+    $( Nest the composition of two substitutions.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ sbcnestgw
+       when possible.  (Contributed by NM, 27-Nov-2005.)  (Proof shortened by
+       Mario Carneiro, 11-Nov-2016.)  (New usage is discouraged.) $)
     sbcnestg $p |- ( A e. V ->
           ( [. A / x ]. [. B / y ]. ph <-> [. [_ A / x ]_ B / y ]. ph ) ) $=
       ( wcel wnf wal wsbc csb wb nfv ax-gen sbcnestgf mpan2 ) DFGABHZCIACEJBDJA
       CBDEKJLQCABMNABCDEFOP $.
 
     $d x C $.
-    $( Nest the composition of two substitutions.  (Contributed by NM,
-       23-Nov-2005.)  (Proof shortened by Mario Carneiro, 10-Nov-2016.)
-       (New usage is discouraged.) $)
+    $( Nest the composition of two substitutions.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ csbnestgw
+       when possible.  (Contributed by NM, 23-Nov-2005.)  (Proof shortened by
+       Mario Carneiro, 10-Nov-2016.)  (New usage is discouraged.) $)
     csbnestg $p |- ( A e. V ->
           [_ A / x ]_ [_ B / y ]_ C = [_ [_ A / x ]_ B / y ]_ C ) $=
       ( wcel wnfc wal csb wceq nfcv ax-gen csbnestgf mpan2 ) CFGAEHZBIACBDEJJBA
@@ -40411,16 +40716,18 @@ among classes ( ~ eq0 , as opposed to the weaker uniqueness among sets,
   ${
     $d x A $.  $d x ph $.  $d x C $.  $d x D $.
     sbcco3g.1 $e |- ( x = A -> B = C ) $.
-    $( Composition of two substitutions.  (Contributed by NM, 27-Nov-2005.)
-       (Revised by Mario Carneiro, 11-Nov-2016.)
-       (New usage is discouraged.) $)
+    $( Composition of two substitutions.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ sbcco3gw when
+       possible.  (Contributed by NM, 27-Nov-2005.)  (Revised by Mario
+       Carneiro, 11-Nov-2016.)  (New usage is discouraged.) $)
     sbcco3g $p |- ( A e. V ->
          ( [. A / x ]. [. B / y ]. ph <-> [. C / y ]. ph ) ) $=
       ( wcel wsbc csb sbcnestg cvv wceq wb elex nfcvd csbiegf dfsbcq 3syl bitrd
       ) DGIZACEJBDJACBDEKZJZACFJZABCDEGLUBDMIZUCFNUDUEODGPBDEFMUFBFQHRACUCFSTUA
       $.
 
-    $( Composition of two class substitutions.  (Contributed by NM,
+    $( Composition of two class substitutions.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  (Contributed by NM,
        27-Nov-2005.)  (Revised by Mario Carneiro, 11-Nov-2016.)
        (New usage is discouraged.) $)
     csbco3g $p |- ( A e. V ->
@@ -45615,15 +45922,17 @@ same distinct variable group (meaning ` A ` cannot depend on ` x ` ) and
     $d z A $.  $d z B $.  $d x z $.  $d y z $.
     nfiung.1 $e |- F/_ y A $.
     nfiung.2 $e |- F/_ y B $.
-    $( Bound-variable hypothesis builder for indexed union.  See ~ nfiun for a
-       version with more disjoint variable conditions, but not requiring
+    $( Bound-variable hypothesis builder for indexed union.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  See ~ nfiun for
+       a version with more disjoint variable conditions, but not requiring
        ~ ax-13 .  (Contributed by Mario Carneiro, 25-Jan-2014.)
        (New usage is discouraged.) $)
     nfiung $p |- F/_ y U_ x e. A B $=
       ( vz ciun cv wcel wrex cab df-iun nfcri nfrexg nfabg nfcxfr ) BACDHGIDJZA
       CKZGLAGCDMSBGRBACEBGDFNOPQ $.
 
-    $( Bound-variable hypothesis builder for indexed intersection.  See ~ nfiin
+    $( Bound-variable hypothesis builder for indexed intersection.  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .  See ~ nfiin
        for a version with more disjoint variable conditions, but not requiring
        ~ ax-13 .  (Contributed by Mario Carneiro, 25-Jan-2014.)
        (New usage is discouraged.) $)
@@ -45753,8 +46062,9 @@ same distinct variable group (meaning ` A ` cannot depend on ` x ` ) and
     cbviung.2 $e |- F/_ x C $.
     cbviung.3 $e |- ( x = y -> B = C ) $.
     $( Rule used to change the bound variables in an indexed union, with the
-       substitution specified implicitly by the hypothesis.  See ~ cbviun for a
-       version with more disjoint variable conditions, but not requiring
+       substitution specified implicitly by the hypothesis.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  See ~ cbviun for
+       a version with more disjoint variable conditions, but not requiring
        ~ ax-13 .  (Contributed by NM, 26-Mar-2006.)  (Revised by Andrew Salmon,
        25-Jul-2011.)  (New usage is discouraged.) $)
     cbviung $p |- U_ x e. A B = U_ y e. A C $=
@@ -45762,8 +46072,9 @@ same distinct variable group (meaning ` A ` cannot depend on ` x ` ) and
       IJZDKZACLZIMUBEKZBCLZIMACDNBCENUDUFIUCUEABCBIDFOAIEGOABPDEUBHQRSAICDTBICE
       TUA $.
 
-    $( Change bound variables in an indexed intersection.  See ~ cbviin for a
-       version with more disjoint variable conditions, but not requiring
+    $( Change bound variables in an indexed intersection.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  See ~ cbviin for
+       a version with more disjoint variable conditions, but not requiring
        ~ ax-13 .  (Contributed by Jeff Hankins, 26-Aug-2009.)  (Revised by
        Mario Carneiro, 14-Oct-2016.)  (New usage is discouraged.) $)
     cbviing $p |- |^|_ x e. A B = |^|_ y e. A C $=
@@ -45797,13 +46108,17 @@ same distinct variable group (meaning ` A ` cannot depend on ` x ` ) and
     $d x A $.  $d y A $.  $d y B $.  $d x C $.
     cbviunvg.1 $e |- ( x = y -> B = C ) $.
     $( Rule used to change the bound variables in an indexed union, with the
-       substitution specified implicitly by the hypothesis.  (Contributed by
-       NM, 15-Sep-2003.)  (New usage is discouraged.) $)
+       substitution specified implicitly by the hypothesis.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  Usage of the
+       weaker ~ cbviunv is preferred.  (Contributed by NM, 15-Sep-2003.)
+       (New usage is discouraged.) $)
     cbviunvg $p |- U_ x e. A B = U_ y e. A C $=
       ( nfcv cbviung ) ABCDEBDGAEGFH $.
 
-    $( Change bound variables in an indexed intersection.  (Contributed by Jeff
-       Hankins, 26-Aug-2009.)  (New usage is discouraged.) $)
+    $( Change bound variables in an indexed intersection.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  Usage of the
+       weaker ~ cbviinv is preferred.  (Contributed by Jeff Hankins,
+       26-Aug-2009.)  (New usage is discouraged.) $)
     cbviinvg $p |- |^|_ x e. A B = |^|_ y e. A C $=
       ( nfcv cbviing ) ABCDEBDGAEGFH $.
   $}
@@ -46526,8 +46841,10 @@ same distinct variable group (meaning ` A ` cannot depend on ` x ` ) and
     $d z A $.  $d z B $.  $d x z $.  $d y z $.
     nfdisj.1 $e |- F/_ y A $.
     nfdisj.2 $e |- F/_ y B $.
-    $( Bound-variable hypothesis builder for disjoint collection.  (Contributed
-       by Mario Carneiro, 14-Nov-2016.)  (New usage is discouraged.) $)
+    $( Bound-variable hypothesis builder for disjoint collection.  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ nfdisjw when possible.  (Contributed by Mario Carneiro,
+       14-Nov-2016.)  (New usage is discouraged.) $)
     nfdisj $p |- F/ y Disj_ x e. A B $=
       ( vz wdisj cv wcel wa wmo wal dfdisj2 wnf wtru nftru weq wn a1i wnfc nfal
       nfcvf nfeld nfcri nfand adantl nfmod2 mptru nfxfr ) ACDHAIZCJZGIDJZKZALZG
@@ -46823,29 +47140,29 @@ same distinct variable group (meaning ` A ` cannot depend on ` x ` ) and
     $d w x y z A $.  $d w x y z B $.  $d w y z C $.  $d w x z D $.
     disjxun.1 $e |- ( x = y -> C = D ) $.
     $( The union of two disjoint collections.  (Contributed by Mario Carneiro,
-       14-Nov-2016.)  (New usage is discouraged.) $)
+       14-Nov-2016.) $)
     disjxun $p |- ( ( A i^i B ) = (/) -> ( Disj_ x e. ( A u. B ) C <->
       ( Disj_ x e. A C /\ Disj_ x e. B C /\
         A. x e. A A. y e. B ( C i^i D ) = (/) ) ) ) $=
       ( vz vw cin c0 wceq weq cv wo wral wa eqeq1d orbi12d bitri csb wdisj wcel
       cun w3a wn wb disjel eleq1w notbid syl5ibcom con2d biorf bicomd 2ralbidva
-      impr syl anbi2d ralunb ralbii nfv nfcv nfcsb1v nfin nfeq1 equequ2 csbhypf
-      nfral ineq2d cbvralv equequ1 csbeq1a ineq1d ralbidv syl5bbr cbvral r19.26
-      3bitr3i disjor anbi1i 3bitr4g equcom syl6bb syl6eq ralcom disjors anbi2ci
-      nfor incom syl5bb anbi1d anbi12d df-3an anandir ) CDJKLZHIMZAHNZEUAZAINZE
-      UAZJZKLZOZICDUDZPZHCPZXEHDPZQZACEUBZEFJZKLZBDPACPZQZADEUBZXLQZQZAXDEUBZXI
-      XNXLUEZWOXFXMXGXOWOABMZXKOZBCPZACPZXTBDPZACPZQZYBXLQXFXMWOYDXLYBWOXTXKABC
-      DWOANZCUCZBNZDUCZQQZXKXTYJXSUFZXKXTUGWOYGYIYKWOYGQZXSYIYLYFDUCZUFXSYIUFCD
-      YFUHXSYMYIABDUIUJUKULUPXSXKUMUQUNUOZURXTBXDPZACPYAYCQZACPXFYEYOYPACXTBCDU
-      SUTYOXEAHCYOHVAXCAIXDAXDVBWPXBAWPAVAAXAKAWRWTAWQEVCAWSEVCVDVEWHZVHYOAIMZE
-      WTJZKLZOZIXDPAHMZXEUUAXTIBXDIBMZYRXSYTXKIBAVFUUCYSXJKUUCWTFEAIYHEFAYHVBZA
-      FVBZGVGVIRSVJUUBUUAXCIXDUUBYRWPYTXBAHIVKUUBYSXAKUUBEWRWTAWQEVLVMRSVNVOVPY
-      AYCACVQVRXIYBXLCEFABGVSVTWAWOXCICPZHDPZXCIDPZHDPZQZXLUUIQXGXOWOUUGXLUUIUU
-      GYDWOXLUUGXTACPZBDPYDUUFUUKHBDUUFHAMZWREJZKLZOZACPHBMZUUKUUOXCAICUUOIVAYQ
-      YRUULWPUUNXBAIHVFYRUUMXAKYREWTWRAWSEVLVIRSVPUUPUUOXTACUUPUULXSUUNXKUUPUUL
-      BAMXSHBAVKBAWBWCUUPUUMXJKUUPUUMFEJXJUUPWRFEAHYHEFUUDUUEGVGVMFEWIWDRSVNVOV
-      JXTBADCWETYNWJWKXGUUFUUHQZHDPUUJXEUUQHDXCICDUSUTUUFUUHHDVQTXNUUIXLADEHIWF
-      WGWAWLXQXEHXDPXHAXDEHIWFXEHCDUSTXRXIXNQXLQXPXIXNXLWMXIXNXLWNTWA $.
+      impr syl anbi2d ralunb ralbii nfcv nfcsb1v nfin nfeq1 nfor nfralw equequ2
+      nfv csbhypf ineq2d cbvralvw equequ1 csbeq1a ineq1d ralbidv syl5bbr r19.26
+      cbvralw 3bitr3i disjor anbi1i 3bitr4g equcom syl6bb syl6eq ralcom disjors
+      incom syl5bb anbi1d anbi2ci anbi12d df-3an anandir ) CDJKLZHIMZAHNZEUAZAI
+      NZEUAZJZKLZOZICDUDZPZHCPZXEHDPZQZACEUBZEFJZKLZBDPACPZQZADEUBZXLQZQZAXDEUB
+      ZXIXNXLUEZWOXFXMXGXOWOABMZXKOZBCPZACPZXTBDPZACPZQZYBXLQXFXMWOYDXLYBWOXTXK
+      ABCDWOANZCUCZBNZDUCZQQZXKXTYJXSUFZXKXTUGWOYGYIYKWOYGQZXSYIYLYFDUCZUFXSYIU
+      FCDYFUHXSYMYIABDUIUJUKULUPXSXKUMUQUNUOZURXTBXDPZACPYAYCQZACPXFYEYOYPACXTB
+      CDUSUTYOXEAHCYOHVHXCAIXDAXDVAWPXBAWPAVHAXAKAWRWTAWQEVBAWSEVBVCVDVEZVFYOAI
+      MZEWTJZKLZOZIXDPAHMZXEUUAXTIBXDIBMZYRXSYTXKIBAVGUUCYSXJKUUCWTFEAIYHEFAYHV
+      AZAFVAZGVIVJRSVKUUBUUAXCIXDUUBYRWPYTXBAHIVLUUBYSXAKUUBEWRWTAWQEVMVNRSVOVP
+      VRYAYCACVQVSXIYBXLCEFABGVTWAWBWOXCICPZHDPZXCIDPZHDPZQZXLUUIQXGXOWOUUGXLUU
+      IUUGYDWOXLUUGXTACPZBDPYDUUFUUKHBDUUFHAMZWREJZKLZOZACPHBMZUUKUUOXCAICUUOIV
+      HYQYRUULWPUUNXBAIHVGYRUUMXAKYREWTWRAWSEVMVJRSVRUUPUUOXTACUUPUULXSUUNXKUUP
+      UULBAMXSHBAVLBAWCWDUUPUUMXJKUUPUUMFEJXJUUPWRFEAHYHEFUUDUUEGVIVNFEWHWERSVO
+      VPVKXTBADCWFTYNWIWJXGUUFUUHQZHDPUUJXEUUQHDXCICDUSUTUUFUUHHDVQTXNUUIXLADEH
+      IWGWKWBWLXQXEHXDPXHAXDEHIWGXEHCDUSTXRXIXNQXLQXPXIXNXLWMXIXNXLWNTWB $.
   $}
 
   ${
@@ -47535,7 +47852,8 @@ although the definition does not require it (see ~ dfid2 for a case
     cbvopab1g.2 $e |- F/ x ps $.
     cbvopab1g.3 $e |- ( x = z -> ( ph <-> ps ) ) $.
     $( Change first bound variable in an ordered-pair class abstraction, using
-       explicit substitution.  See ~ cbvopab1 for a version with more disjoint
+       explicit substitution.  Usage of this theorem is discouraged because it
+       depends on ~ ax-13 .  See ~ cbvopab1 for a version with more disjoint
        variable conditions, but not requiring ~ ax-13 .  (Contributed by NM,
        6-Oct-2004.)  (Revised by Mario Carneiro, 14-Oct-2016.)
        (New usage is discouraged.) $)
@@ -47828,7 +48146,8 @@ although the definition does not require it (see ~ dfid2 for a case
     cbvmptfg.5 $e |- ( x = y -> B = C ) $.
     $( Rule to change the bound variable in a maps-to function, using implicit
        substitution.  This version has bound-variable hypotheses in place of
-       distinct variable conditions.  See ~ cbvmptf for a version with more
+       distinct variable conditions.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  See ~ cbvmptf for a version with more
        disjoint variable conditions, but not requiring ~ ax-13 .  (Contributed
        by NM, 11-Sep-2011.)  (Revised by Thierry Arnoux, 9-Mar-2017.)
        (New usage is discouraged.) $)
@@ -47864,7 +48183,8 @@ although the definition does not require it (see ~ dfid2 for a case
     cbvmptg.3 $e |- ( x = y -> B = C ) $.
     $( Rule to change the bound variable in a maps-to function, using implicit
        substitution.  This version has bound-variable hypotheses in place of
-       distinct variable conditions.  See ~ cbvmpt for a version with more
+       distinct variable conditions.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  See ~ cbvmpt for a version with more
        disjoint variable conditions, but not requiring ~ ax-13 .  (Contributed
        by NM, 11-Sep-2011.)  (New usage is discouraged.) $)
     cbvmptg $p |- ( x e. A |-> B ) = ( y e. A |-> C ) $=
@@ -47888,7 +48208,8 @@ although the definition does not require it (see ~ dfid2 for a case
     $d A x $.  $d A y $.  $d B y $.  $d C x $.
     cbvmptvg.1 $e |- ( x = y -> B = C ) $.
     $( Rule to change the bound variable in a maps-to function, using implicit
-       substitution.  See ~ cbvmptv for a version with more disjoint variable
+       substitution.  Usage of this theorem is discouraged because it depends
+       on ~ ax-13 .  See ~ cbvmptv for a version with more disjoint variable
        conditions, but not requiring ~ ax-13 .  (Contributed by Mario Carneiro,
        19-Feb-2013.)  (New usage is discouraged.) $)
     cbvmptvg $p |- ( x e. A |-> B ) = ( y e. A |-> C ) $=
@@ -49040,7 +49361,8 @@ This theorem is proved directly from set theory axioms (no set theory
   ${
     dtrucor2.1 $e |- ( x = y -> x =/= y ) $.
     $( The theorem form of the deduction ~ dtrucor leads to a contradiction, as
-       mentioned in the "Wrong!" example at ~ mmdeduction.html#bad .
+       mentioned in the "Wrong!" example at ~ mmdeduction.html#bad .  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 20-Oct-2007.)  (New usage is discouraged.) $)
     dtrucor2 $p |- ( ph /\ -. ph ) $=
       ( weq wex wn wa ax6e wi cv necon2bi pm2.01 ax-mp nex pm2.24ii ) BCEZBFAAG
@@ -49119,7 +49441,8 @@ That theorem bundles the theorems ( ` |- E. x ( x = y -> z e. x ) ` with
   $( The "distinctor" expression ` -. A. x x = y ` , stating that ` x ` and
      ` y ` are not the same variable, can be written in terms of ` F/ ` in the
      obvious way.  This theorem is not true in a one-element domain, because
-     then ` F/_ x y ` and ` A. x x = y ` will both be true.  (Contributed by
+     then ` F/_ x y ` and ` A. x x = y ` will both be true.  Usage of this
+     theorem is discouraged because it depends on ~ ax-13 .  (Contributed by
      Mario Carneiro, 8-Oct-2016.)  (New usage is discouraged.) $)
   nfcvb $p |- ( F/_ x y <-> -. A. x x = y ) $=
     ( cv wnfc weq wal wn nfnid eqidd drnfc1 mtbiri con2i nfcvf impbii ) ABCZDZA
@@ -50278,10 +50601,11 @@ That theorem bundles the theorems ( ` |- E. x ( x = y -> z e. x ) ` with
 
   ${
     $d x z w A $.  $d y z w A $.  $d z w ph $.
-    $( Substitution of class ` A ` for ordered pair ` <. x , y >. ` .
-       (Contributed by NM, 27-Dec-1996.)  (Revised by Andrew Salmon,
-       11-Jul-2011.)  (Proof shortened by Wolf Lammen, 25-Aug-2019.)
-       (New usage is discouraged.) $)
+    $( Substitution of class ` A ` for ordered pair ` <. x , y >. ` .  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ copsexgw when possible.  (Contributed by NM, 27-Dec-1996.)
+       (Revised by Andrew Salmon, 11-Jul-2011.)  (Proof shortened by Wolf
+       Lammen, 25-Aug-2019.)  (New usage is discouraged.) $)
     copsexg $p |- ( A = <. x , y >. ->
                   ( ph <-> E. x E. y ( A = <. x , y >. /\ ph ) ) ) $=
       ( vz vw cv cop wceq wa wex wb wi vex 19.8a weq syl5 syl5bi weu euequ opth
@@ -50779,8 +51103,10 @@ necessary if all involved classes exist as sets (i.e. are not proper
   ${
     $d x z $.  $d y z $.  $d ph z $.
     $( The law of concretion.  Special case of Theorem 9.5 of [Quine] p. 61.
-       (Contributed by NM, 14-Apr-1995.)  (Proof shortened by Andrew Salmon,
-       25-Jul-2011.)  (New usage is discouraged.) $)
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       Use the weaker ~ opabidw when possible.  (Contributed by NM,
+       14-Apr-1995.)  (Proof shortened by Andrew Salmon, 25-Jul-2011.)
+       (New usage is discouraged.) $)
     opabid $p |- ( <. x , y >. e. { <. x , y >. | ph } <-> ph ) $=
       ( vz cv cop wceq wa wex copab opex copsexg bicomd df-opab elab2 ) DEZBEZC
       EZFZGZAHCIBIZADSABCJQRKTAUAABCPLMABCDNO $.
@@ -51050,9 +51376,11 @@ necessary if all involved classes exist as sets (i.e. are not proper
     $( $j usage 'eqopab2bw' avoids 'ax-13'; $)
   $}
 
-  $( Equivalence of ordered pair abstraction subclass and implication.
-     (Contributed by NM, 27-Dec-1996.)  (Proof shortened by Mario Carneiro,
-     18-Nov-2016.)  (New usage is discouraged.) $)
+  $( Equivalence of ordered pair abstraction subclass and implication.  Usage
+     of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+     weaker ~ ssopab2bw when possible.  (Contributed by NM, 27-Dec-1996.)
+     (Proof shortened by Mario Carneiro, 18-Nov-2016.)
+     (New usage is discouraged.) $)
   ssopab2b $p |- ( { <. x , y >. | ph } C_ { <. x , y >. | ps } <->
                A. x A. y ( ph -> ps ) ) $=
     ( copab wss wi wal nfopab1 nfss nfopab2 cop wcel ssel opabid 3imtr3g alrimi
@@ -51078,9 +51406,10 @@ necessary if all involved classes exist as sets (i.e. are not proper
       $.
   $}
 
-  $( Equivalence of ordered pair abstraction equality and biconditional.
-     (Contributed by Mario Carneiro, 4-Jan-2017.)
-     (New usage is discouraged.) $)
+  $( Equivalence of ordered pair abstraction equality and biconditional.  Usage
+     of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+     weaker ~ eqopab2bw when possible.  (Contributed by Mario Carneiro,
+     4-Jan-2017.)  (New usage is discouraged.) $)
   eqopab2b $p |- ( { <. x , y >. | ph } = { <. x , y >. | ps }
                 <-> A. x A. y ( ph <-> ps ) ) $=
     ( copab wss wa wi wal wceq wb ssopab2b anbi12i eqss 2albiim 3bitr4i ) ACDEZ
@@ -58988,7 +59317,9 @@ Definite description binder (inverted iota)
     $d z ps $.  $d z ph $.  $d x z $.  $d y z $.
     nfiotad.1 $e |- F/ y ph $.
     nfiotad.2 $e |- ( ph -> F/ x ps ) $.
-    $( Deduction version of ~ nfiota .  (Contributed by NM, 18-Feb-2013.)
+    $( Deduction version of ~ nfiota .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ nfiotadw when
+       possible.  (Contributed by NM, 18-Feb-2013.)
        (New usage is discouraged.) $)
     nfiotad $p |- ( ph -> F/_ x ( iota y ps ) ) $=
       ( vz cio weq wb wal cab cuni dfiota2 nfv wn wa wnf adantr nfeqf1 nfcxfrd
@@ -58998,8 +59329,10 @@ Definite description binder (inverted iota)
 
   ${
     nfiota.1 $e |- F/ x ph $.
-    $( Bound-variable hypothesis builder for the ` iota ` class.  (Contributed
-       by NM, 23-Aug-2011.)  (New usage is discouraged.) $)
+    $( Bound-variable hypothesis builder for the ` iota ` class.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  Use the weaker
+       ~ nfiotaw when possible.  (Contributed by NM, 23-Aug-2011.)
+       (New usage is discouraged.) $)
     nfiota $p |- F/_ x ( iota y ph ) $=
       ( cio wnfc wtru nftru wnf a1i nfiotad mptru ) BACEFGABCCHABIGDJKL $.
   $}
@@ -59035,8 +59368,10 @@ Definite description binder (inverted iota)
     cbviota.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
     cbviota.2 $e |- F/ y ph $.
     cbviota.3 $e |- F/ x ps $.
-    $( Change bound variables in a description binder.  (Contributed by Andrew
-       Salmon, 1-Aug-2011.)  (New usage is discouraged.) $)
+    $( Change bound variables in a description binder.  Usage of this theorem
+       is discouraged because it depends on ~ ax-13 .  Use the weaker
+       ~ cbviotaw when possible.  (Contributed by Andrew Salmon, 1-Aug-2011.)
+       (New usage is discouraged.) $)
     cbviota $p |- ( iota x ph ) = ( iota y ps ) $=
       ( vw vz weq wb wal cab cuni cio wsb nfv nfbi equequ1 bibi12d sbequ12 nfsb
       nfs1v cbvalv1 sbequ sbie syl6bb bitri abbii unieqi dfiota2 3eqtr4i ) ACHJ
@@ -59048,8 +59383,10 @@ Definite description binder (inverted iota)
   ${
     $d ph y $.  $d ps x $.
     cbviotav.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( Change bound variables in a description binder.  (Contributed by Andrew
-       Salmon, 1-Aug-2011.)  (New usage is discouraged.) $)
+    $( Change bound variables in a description binder.  Usage of this theorem
+       is discouraged because it depends on ~ ax-13 .  Use the weaker
+       ~ cbviotavw when possible.  (Contributed by Andrew Salmon, 1-Aug-2011.)
+       (New usage is discouraged.) $)
     cbviotav $p |- ( iota x ph ) = ( iota y ps ) $=
       ( nfv cbviota ) ABCDEADFBCFG $.
   $}
@@ -59057,7 +59394,8 @@ Definite description binder (inverted iota)
   ${
     $d w z ph $.  $d w z x $.  $d w z y $.
     sb8iota.1 $e |- F/ y ph $.
-    $( Variable substitution in description binder.  Compare ~ sb8eu .
+    $( Variable substitution in description binder.  Compare ~ sb8eu .  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 18-Mar-2013.)  (New usage is discouraged.) $)
     sb8iota $p |- ( iota x ph ) = ( iota y [ y / x ] ph ) $=
       ( vz vw weq wal cab cuni wsb cio nfv sb8 sbbi nfsb equsb3 nfxfr dfiota2
@@ -59069,7 +59407,8 @@ Definite description binder (inverted iota)
 
   ${
     $d y z $.  $d x z $.  $d ph z $.
-    $( Equality theorem for descriptions.  (Contributed by Andrew Salmon,
+    $( Equality theorem for descriptions.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by Andrew Salmon,
        30-Jun-2011.)  (New usage is discouraged.) $)
     iotaeq $p |- ( A. x x = y -> ( iota x ph ) = ( iota y ph ) ) $=
       ( vz cv wceq wal cab csn cuni cio wcel drsb1 df-clab 3bitr4g eqrdv eqeq1d
@@ -63340,8 +63679,9 @@ empty set when it is not meaningful (as shown by ~ ndmfv and ~ fvprc ).
     $( Implications for the value of a function defined by the maps-to notation
        with a class abstraction as a result having an element.  Here, the base
        set of the class abstraction depends on the argument of the function.
-       (Contributed by Alexander van der Vekens, 15-Jul-2018.)
-       (New usage is discouraged.) $)
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       Use the weaker ~ elfvmptrab1w when possible.  (Contributed by Alexander
+       van der Vekens, 15-Jul-2018.)  (New usage is discouraged.) $)
     elfvmptrab1 $p |- ( Y e. ( F ` X )
                         -> ( X e. V /\ Y e. [_ X / m ]_ M ) ) $=
       ( cfv wcel csb c0 crab cvv wceq 3syl nfcv wa wne ne0i ndmfv necon1ai wsbc
@@ -64095,8 +64435,10 @@ in the range of the function (the implication "to the right" is always
     $d w x z A $.  $d y B $.  $d y ch $.  $d w y z F $.  $d w x z ps $.
     ralrnmpt.1 $e |- F = ( x e. A |-> B ) $.
     ralrnmpt.2 $e |- ( y = B -> ( ps <-> ch ) ) $.
-    $( A restricted quantifier over an image set.  (Contributed by Mario
-       Carneiro, 20-Aug-2015.)  (New usage is discouraged.) $)
+    $( A restricted quantifier over an image set.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ ralrnmptw
+       when possible.  (Contributed by Mario Carneiro, 20-Aug-2015.)
+       (New usage is discouraged.) $)
     ralrnmpt $p |- ( A. x e. A B e. V ->
       ( A. y e. ran F ps <-> A. x e. A ch ) ) $=
       ( vw vz wcel wral cv cfv wsbc wb syl nfv crn fnmpt dfsbcq nfsbc1v sbceq1a
@@ -64107,8 +64449,10 @@ in the range of the function (the implication "to the right" is always
       FUKULCVSUMURACTUNVMLTLCUOADVTVLVSVKGUSUPUHUQVHVMBRZCENVNVORVGWCCEVKEMZVGU
       TZVMADFQZBWEADVLFCEFHGIVAUPVGWFBRWDABDFHJVBVCVDVEVMBCEVFSVD $.
 
-    $( A restricted quantifier over an image set.  (Contributed by Mario
-       Carneiro, 20-Aug-2015.)  (New usage is discouraged.) $)
+    $( A restricted quantifier over an image set.  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  Use the weaker ~ rexrnmptw
+       when possible.  (Contributed by Mario Carneiro, 20-Aug-2015.)
+       (New usage is discouraged.) $)
     rexrnmpt $p |- ( A. x e. A B e. V ->
       ( E. y e. ran F ps <-> E. x e. A ch ) ) $=
       ( wcel wral wn crn wrex cv wceq notbid ralrnmpt dfrex2 3bitr4g ) FHKCELZA
@@ -67539,9 +67883,10 @@ Restricted iota (description binder)
     nfriotad.1 $e |- F/ y ph $.
     nfriotad.2 $e |- ( ph -> F/ x ps ) $.
     nfriotad.3 $e |- ( ph -> F/_ x A ) $.
-    $( Deduction version of ~ nfriota .  (Contributed by NM, 18-Feb-2013.)
-       (Revised by Mario Carneiro, 15-Oct-2016.)
-       (New usage is discouraged.) $)
+    $( Deduction version of ~ nfriota .  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  Use the weaker ~ nfriotadw when
+       possible.  (Contributed by NM, 18-Feb-2013.)  (Revised by Mario
+       Carneiro, 15-Oct-2016.)  (New usage is discouraged.) $)
     nfriotad $p |- ( ph -> F/_ x ( iota_ y e. A ps ) ) $=
       ( crio cv wcel wa cio df-riota weq wal wnfc wn nfnae adantr nfcvf nfiotad
       nfan adantl nfeld wnf nfand nfiota1 eqidd drnfc1 mpbiri pm2.61d2 nfcxfrd
@@ -67566,9 +67911,10 @@ Restricted iota (description binder)
     cbvriota.1 $e |- F/ y ph $.
     cbvriota.2 $e |- F/ x ps $.
     cbvriota.3 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( Change bound variable in a restricted description binder.  (Contributed
-       by NM, 18-Mar-2013.)  (Revised by Mario Carneiro, 15-Oct-2016.)
-       (New usage is discouraged.) $)
+    $( Change bound variable in a restricted description binder.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  Use the weaker
+       ~ cbvriotaw when possible.  (Contributed by NM, 18-Mar-2013.)  (Revised
+       by Mario Carneiro, 15-Oct-2016.)  (New usage is discouraged.) $)
     cbvriota $p |- ( iota_ x e. A ph ) = ( iota_ y e. A ps ) $=
       ( vz cv wcel wa cio crio wsb weq eleq1w anbi12d nfv nfan nfs1v sbequ sbie
       sbequ12 cbviota syl6bb nfsb eqtri df-riota 3eqtr4i ) CJEKZALZCMZDJEKZBLZD
@@ -67580,9 +67926,10 @@ Restricted iota (description binder)
   ${
     $d x A $.  $d y A $.  $d y ph $.  $d x ps $.
     cbvriotav.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
-    $( Change bound variable in a restricted description binder.  (Contributed
-       by NM, 18-Mar-2013.)  (Revised by Mario Carneiro, 15-Oct-2016.)
-       (New usage is discouraged.) $)
+    $( Change bound variable in a restricted description binder.  Usage of this
+       theorem is discouraged because it depends on ~ ax-13 .  Use the weaker
+       ~ cbvriotavw when possible.  (Contributed by NM, 18-Mar-2013.)  (Revised
+       by Mario Carneiro, 15-Oct-2016.)  (New usage is discouraged.) $)
     cbvriotav $p |- ( iota_ x e. A ph ) = ( iota_ y e. A ps ) $=
       ( nfv cbvriota ) ABCDEADGBCGFH $.
   $}
@@ -68203,8 +68550,9 @@ ordered pairs (for use in defining operations).  This is a special case
   ${
     $d a ph r s t w $.  $d a r s t w x $.  $d a r s t w y $.  $d a r s t w z $.
     $( The law of concretion.  Special case of Theorem 9.5 of [Quine] p. 61.
-       (Contributed by Mario Carneiro, 20-Mar-2013.)
-       (New usage is discouraged.) $)
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       Use the weaker ~ oprabidw when possible.  (Contributed by Mario
+       Carneiro, 20-Mar-2013.)  (New usage is discouraged.) $)
     oprabid $p |- ( <. <. x , y >. , z >. e.
         { <. <. x , y >. , z >. | ph } <-> ph ) $=
       ( vw va vt vr vs cv cop wceq wa wex wi vex weq weu euequ eupick eqeq1 w3a
@@ -68590,7 +68938,8 @@ ordered pairs (for use in defining operations).  This is a special case
   $}
 
   $( Equivalence of ordered pair abstraction subclass and implication.  Compare
-     ~ ssopab2b .  (Contributed by FL, 6-Nov-2013.)  (Proof shortened by Mario
+     ~ ssopab2b .  Usage of this theorem is discouraged because it depends on
+     ~ ax-13 .  (Contributed by FL, 6-Nov-2013.)  (Proof shortened by Mario
      Carneiro, 11-Dec-2016.)  (New usage is discouraged.) $)
   ssoprab2b $p |- ( { <. <. x , y >. , z >. | ph } C_
     { <. <. x , y >. , z >. | ps } <-> A. x A. y A. z ( ph -> ps ) ) $=
@@ -68616,7 +68965,9 @@ ordered pairs (for use in defining operations).  This is a special case
   $}
 
   $( Equivalence of ordered pair abstraction subclass and biconditional.
-     Compare ~ eqopab2b .  (Contributed by Mario Carneiro, 4-Jan-2017.)
+     Compare ~ eqopab2b .  Usage of this theorem is discouraged because it
+     depends on ~ ax-13 .  Use the weaker ~ eqoprab2bw when possible.
+     (Contributed by Mario Carneiro, 4-Jan-2017.)
      (New usage is discouraged.) $)
   eqoprab2b $p |- ( { <. <. x , y >. , z >. | ph } =
     { <. <. x , y >. , z >. | ps } <-> A. x A. y A. z ( ph <-> ps ) ) $=
@@ -70645,8 +70996,9 @@ result of an operator (deduction version).  (Contributed by Paul
     $( Implications for the value of an operation, defined by the maps-to
        notation with a class abstraction as a result, having an element.  Here,
        the base set of the class abstraction depends on the first operand.
-       (Contributed by Alexander van der Vekens, 15-Jul-2018.)
-       (New usage is discouraged.) $)
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
+       Use the weaker ~ elovmporab1w when possible.  (Contributed by Alexander
+       van der Vekens, 15-Jul-2018.)  (New usage is discouraged.) $)
     elovmporab1 $p |- ( Z e. ( X O Y )
                          -> ( X e. _V /\ Y e. _V /\ Z e. [_ X / m ]_ M ) ) $=
       ( cvv wcel wa csb cv wceq nfcv nfel1 co w3a crab elmpocl wsbc cmpo csbeq1
@@ -85036,9 +85388,10 @@ the first case of his notation (simple exponentiation) and subscript it
     $d x z $.  $d y z $.  $d A z $.  $d B z $.
     nfixp.1 $e |- F/_ y A $.
     nfixp.2 $e |- F/_ y B $.
-    $( Bound-variable hypothesis builder for indexed Cartesian product.
-       (Contributed by Mario Carneiro, 15-Oct-2016.)
-       (New usage is discouraged.) $)
+    $( Bound-variable hypothesis builder for indexed Cartesian product.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ nfixpw when possible.  (Contributed by Mario Carneiro,
+       15-Oct-2016.)  (New usage is discouraged.) $)
     nfixp $p |- F/_ y X_ x e. A B $=
       ( vz cixp cv wcel cab wfn cfv wa wnfc wtru wal a1i nfeld mptru wral nftru
       df-ixp nfcv weq wn nfcvf adantl nfabd2 nffn df-ral wnf nffvd nfimd nfald2
@@ -108832,13 +109185,15 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
 #*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#
 $)
 
-  $( A lemma for proving conditionless ZFC axioms.  (Contributed by NM,
+  $( A lemma for proving conditionless ZFC axioms.  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  (Contributed by NM,
      1-Jan-2002.)  (New usage is discouraged.) $)
   nd1 $p |- ( A. x x = y -> -. A. x y e. z ) $=
     ( weq wal wel elirrv wsb stdpc4 nfnth elequ1 sbie sylib mto axc11 mtoi ) AB
     DAEBCFZAEQBEZRCCFZCGZRQBCHSQBCIQSBCSBTJBCCKLMNQABOP $.
 
-  $( A lemma for proving conditionless ZFC axioms.  (Contributed by NM,
+  $( A lemma for proving conditionless ZFC axioms.  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  (Contributed by NM,
      1-Jan-2002.)  (New usage is discouraged.) $)
   nd2 $p |- ( A. x x = y -> -. A. x z e. y ) $=
     ( weq wal wel elirrv wsb stdpc4 nfnth elequ2 sbie sylib mto axc11 mtoi ) AB
@@ -108850,7 +109205,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
     ( weq wal wel wn elirrv elequ2 mtbii sps sp nsyl ) ABDZAEABFZOCENOGANAAFOAH
     ABAIJKOCLM $.
 
-  $( A lemma for proving conditionless ZFC axioms.  (Contributed by NM,
+  $( A lemma for proving conditionless ZFC axioms.  Usage of this theorem is
+     discouraged because it depends on ~ ax-13 .  (Contributed by NM,
      2-Jan-2002.)  (New usage is discouraged.) $)
   nd4 $p |- ( A. x x = y -> -. A. z y e. x ) $=
     ( wel wal wn nd3 aecoms ) BADCEFBABACGH $.
@@ -108858,7 +109214,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x w $.  $d y w $.  $d z w $.
     $( A version of the Axiom of Extensionality with no distinct variable
-       conditions.  (Contributed by NM, 14-Aug-2003.)
+       conditions.  Usage of this theorem is discouraged because it depends on
+       ~ ax-13 .  (Contributed by NM, 14-Aug-2003.)
        (New usage is discouraged.) $)
     axextnd $p |- E. x ( ( x e. y <-> x e. z ) -> y = z ) $=
       ( vw wel wb weq wal wex wi wn nfnae wnfc nfcvf nfcrd elequ1 syl6 ax6e ax7
@@ -108873,6 +109230,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x z w $.  $d x y w $.  $d w ph $.
     $( Lemma for the Axiom of Replacement with no distinct variable conditions.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 2-Jan-2002.)  (New usage is discouraged.) $)
     axrepndlem1 $p |- ( -. A. y y = z -> E. x ( E. y A. z ( ph -> z = y ) ->
                  A. z ( z e. x <-> E. x ( x e. y /\ A. y ph ) ) ) ) $=
@@ -108890,6 +109248,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x w $.  $d y w $.  $d z w $.  $d w ph $.
     $( Lemma for the Axiom of Replacement with no distinct variable conditions.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 2-Jan-2002.)  (Proof shortened by Mario Carneiro,
        6-Dec-2016.)  (New usage is discouraged.) $)
     axrepndlem2 $p |- ( ( ( -. A. x x = y /\ -. A. x x = z ) /\ -. A. y y = z )
@@ -108911,7 +109270,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   $}
 
   $( A version of the Axiom of Replacement with no distinct variable
-     conditions.  (Contributed by NM, 2-Jan-2002.)
+     conditions.  Usage of this theorem is discouraged because it depends on
+     ~ ax-13 .  (Contributed by NM, 2-Jan-2002.)
      (New usage is discouraged.) $)
   axrepnd $p |- E. x ( E. y A. z ( ph -> z = y ) ->
                A. z ( A. y z e. x <-> E. x ( A. z x e. y /\ A. y ph ) ) ) $=
@@ -108930,6 +109290,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x y w $.  $d x z w $.
     $( Lemma for the Axiom of Union with no distinct variable conditions.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 2-Jan-2002.)  (New usage is discouraged.) $)
     axunndlem1 $p |- E. x A. y ( E. x ( y e. x /\ x e. z ) -> y e. x ) $=
       ( vw weq wal wel wa wi wn cv en2lp elequ2 anbi2d mtbii nexdv nfnae exbidv
@@ -108944,6 +109305,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x w $.  $d y w $.  $d z w $.
     $( A version of the Axiom of Union with no distinct variable conditions.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 2-Jan-2002.)  (New usage is discouraged.) $)
     axunnd $p |- E. x A. y ( E. x ( y e. x /\ x e. z ) -> y e. x ) $=
       ( vw weq wal wel wa wex wi wn nfnae nfan cv wnfc nfcvf adantr nfcvd nfae
@@ -108968,7 +109330,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x w $.  $d z y w $.
     $( Lemma for the Axiom of Power Sets with no distinct variable conditions.
-       Revised to remove a redundant antecedent from the consequence.
+       Revised to remove a redundant antecedent from the consequence.  Usage of
+       this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 4-Jan-2002.)  (Proof shortened by Mario Carneiro,
        6-Dec-2016.)  (Revised and shortened by Wolf Lammen, 9-Jun-2019.)
        (New usage is discouraged.) $)
@@ -108991,6 +109354,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x w $.  $d y z w $.
     $( Lemma for the Axiom of Power Sets with no distinct variable conditions.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 4-Jan-2002.)  (Revised by Mario Carneiro,
        10-Dec-2016.)  (Proof shortened by Wolf Lammen, 10-Jun-2019.)
        (New usage is discouraged.) $)
@@ -109014,6 +109378,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x w $.  $d y w $.  $d z w $.
     $( Lemma for the Axiom of Power Sets with no distinct variable conditions.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 4-Jan-2002.)  (Proof shortened by Mario Carneiro,
        10-Dec-2016.)  (New usage is discouraged.) $)
     axpowndlem4 $p |- ( -. A. y y = x -> ( -. A. y y = z -> ( -. x = y
@@ -109035,7 +109400,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x w $.  $d y w $.
     $( A version of the Axiom of Power Sets with no distinct variable
-       conditions.  (Contributed by NM, 4-Jan-2002.)
+       conditions.  Usage of this theorem is discouraged because it depends on
+       ~ ax-13 .  (Contributed by NM, 4-Jan-2002.)
        (New usage is discouraged.) $)
     axpownd $p |- ( -. x = y ->
                E. x A. y ( A. x ( E. z x e. y -> A. y x e. z ) -> y e. x ) ) $=
@@ -109075,6 +109441,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
 $)
 
   $( Lemma for the Axiom of Regularity with no distinct variable conditions.
+     Usage of this theorem is discouraged because it depends on ~ ax-13 .
      (Contributed by NM, 3-Jan-2002.)  (New usage is discouraged.) $)
   axregndlem1 $p |- ( A. x x = z -> ( x e. y ->
                E. x ( x e. y /\ A. z ( z e. x -> -. z e. y ) ) ) ) $=
@@ -109085,6 +109452,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x w $.  $d z y w $.
     $( Lemma for the Axiom of Regularity with no distinct variable conditions.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 3-Jan-2002.)  (Proof shortened by Mario Carneiro,
        10-Dec-2016.)  (New usage is discouraged.) $)
     axregndlem2 $p |- ( x e. y ->
@@ -109105,7 +109473,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x w $.  $d y w $.  $d z w $.
     $( A version of the Axiom of Regularity with no distinct variable
-       conditions.  (Contributed by NM, 3-Jan-2002.)  (Proof shortened by Wolf
+       conditions.  Usage of this theorem is discouraged because it depends on
+       ~ ax-13 .  (Contributed by NM, 3-Jan-2002.)  (Proof shortened by Wolf
        Lammen, 18-Aug-2019.)  (New usage is discouraged.) $)
     axregnd $p |- ( x e. y ->
                  E. x ( x e. y /\ A. z ( z e. x -> -. z e. y ) ) ) $=
@@ -109159,7 +109528,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
       $.
   $}
 
-  $( Lemma for the Axiom of Choice with no distinct variable conditions.
+  $( Lemma for the Axiom of Choice with no distinct variable conditions.  Usage
+     of this theorem is discouraged because it depends on ~ ax-13 .
      (Contributed by NM, 3-Jan-2002.)  (New usage is discouraged.) $)
   axacndlem1 $p |- ( A. x x = y ->
             E. x A. y A. z ( A. x ( y e. z /\ z e. w ) -> E. w A. y ( E. w
@@ -109168,7 +109538,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
     ) ABEAFZBCGZCDGZHZAFZUCBDGDAGHHDIBDEJBFDIZKZCFZBFATUGBABBLTUFCABCLUDUAAFZTU
     EUCUAAUAUBMNTUHUEABCOPQRRS $.
 
-  $( Lemma for the Axiom of Choice with no distinct variable conditions.
+  $( Lemma for the Axiom of Choice with no distinct variable conditions.  Usage
+     of this theorem is discouraged because it depends on ~ ax-13 .
      (Contributed by NM, 3-Jan-2002.)  (New usage is discouraged.) $)
   axacndlem2 $p |- ( A. x x = z ->
             E. x A. y A. z ( A. x ( y e. z /\ z e. w ) -> E. w A. y ( E. w
@@ -109177,7 +109548,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
     ) ACEAFZBCGZCDGZHZAFZUCBDGDAGHHDIBDEJBFDIZKZCFZBFATUGBACBLTUFCACCLUDUBAFZTU
     EUCUBAUAUBMNTUHUEACDOPQRRS $.
 
-  $( Lemma for the Axiom of Choice with no distinct variable conditions.
+  $( Lemma for the Axiom of Choice with no distinct variable conditions.  Usage
+     of this theorem is discouraged because it depends on ~ ax-13 .
      (Contributed by NM, 3-Jan-2002.)  (New usage is discouraged.) $)
   axacndlem3 $p |- ( A. y y = z ->
             E. x A. y A. z ( A. x ( y e. z /\ z e. w ) -> E. w A. y ( E. w
@@ -109268,12 +109640,14 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
   ${
     $d x y z w v u t $.
     $( Axiom of Extensionality ~ ax-ext , reproved from conditionless ZFC
-       version and predicate calculus.  (Contributed by NM, 15-Aug-2003.)
+       version and predicate calculus.  Usage of this theorem is discouraged
+       because it depends on ~ ax-13 .  (Contributed by NM, 15-Aug-2003.)
        (Proof modification is discouraged.)  (New usage is discouraged.) $)
     zfcndext $p |- ( A. z ( z e. x <-> z e. y ) -> x = y ) $=
       ( cv wcel wb wceq axextnd 19.36iv ) CDZADZEJBDZEFKLGCCABHI $.
 
     $( Axiom of Replacement ~ ax-rep , reproved from conditionless ZFC axioms.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 15-Aug-2003.)  (Proof modification is discouraged.)
        (New usage is discouraged.) $)
     zfcndrep $p |- ( A. w E. y A. z ( A. y ph -> z = y ) ->
@@ -109288,7 +109662,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
       VJCUJWOWDEWNWCVMWCDUJUKTULUMUNTUOUPUQVQWBECWKWAEDVRVTEVREOVSENRSVIVFHZVPW
       ADWTVJVRVOVTECDUAVOVTMWTVNVSEVMVDVLVDCACPURUSTUTVAUGVBVC $.
 
-    $( Axiom of Union ~ ax-un , reproved from conditionless ZFC axioms.
+    $( Axiom of Union ~ ax-un , reproved from conditionless ZFC axioms.  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 15-Aug-2003.)  (Proof modification is discouraged.)
        (New usage is discouraged.) $)
     zfcndun $p |- E. y A. z ( E. w ( z e. w /\ w e. x ) -> z e. y ) $=
@@ -109297,7 +109672,8 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
       BHBCAKUKUPBUJUOCUGUNUIUFUMDBUBUHRUCUIUEULDBCLDBAMNOPQST $.
 
     $( Axiom of Power Sets ~ ax-pow , reproved from conditionless ZFC axioms.
-       The proof uses the "Axiom of Twoness" ~ dtru .  (Contributed by NM,
+       The proof uses the "Axiom of Twoness" ~ dtru .  Usage of this theorem is
+       discouraged because it depends on ~ ax-13 .  (Contributed by NM,
        15-Aug-2003.)  (Proof modification is discouraged.)
        (New usage is discouraged.) $)
     zfcndpow $p |- E. y A. z ( A. w ( w e. z -> w e. x ) -> z e. y ) $=
@@ -109309,6 +109685,7 @@ it contains AC as a simple corollary (letting ` m ( i ) = (/) ` , this
       UHQPRM $.
 
     $( Axiom of Regularity ~ ax-reg , reproved from conditionless ZFC axioms.
+       Usage of this theorem is discouraged because it depends on ~ ax-13 .
        (Contributed by NM, 15-Aug-2003.)  (Proof modification is discouraged.)
        (New usage is discouraged.) $)
     zfcndreg $p |- ( E. y y e. x ->
@@ -166214,9 +166591,11 @@ seq m ( + , ( n e. ZZ |-> if ( n e. A , [_ n / k ]_ B , 0 ) ) ) ~~> x ) \/
     nfsum.1 $e |- F/_ x A $.
     nfsum.2 $e |- F/_ x B $.
     $( Bound-variable hypothesis builder for sum: if ` x ` is (effectively) not
-       free in ` A ` and ` B ` , it is not free in ` sum_ k e. A B ` .
-       (Contributed by NM, 11-Dec-2005.)  (Revised by Mario Carneiro,
-       13-Jun-2019.)  (New usage is discouraged.) $)
+       free in ` A ` and ` B ` , it is not free in ` sum_ k e. A B ` .  Usage
+       of this theorem is discouraged because it depends on ~ ax-13 .  Use the
+       weaker ~ nfsumw when possible.  (Contributed by NM, 11-Dec-2005.)
+       (Revised by Mario Carneiro, 13-Jun-2019.)
+       (New usage is discouraged.) $)
     nfsum $p |- F/_ x sum_ k e. A B $=
       ( vm vn vz vf cv cfv caddc cz csb cc0 cli c1 cn nfcv csu cuz wss wcel cif
       cmpt cseq wbr wa wrex cfz co wf1o wceq wex wo cio df-sum nfss nfcri nfcsb
@@ -756000,8 +756379,9 @@ coordinates of the intersection points of a (nondegenerate) line and a
     nfiundg.3 $e |- ( ph -> F/_ y B ) $.
     $( Bound-variable hypothesis builder for indexed union.  See ~ nfiund for a
        version with more disjoint variable conditions, but not requiring
-       ~ ax-13 .  (Contributed by Emmett Weisz, 6-Dec-2019.)
-       (New usage is discouraged.) $)
+       ~ ax-13 .  Usage of this theorem is discouraged because it depends on
+       ~ ax-13 .  Use the weaker ~ nfiund when possible.  (Contributed by
+       Emmett Weisz, 6-Dec-2019.)  (New usage is discouraged.) $)
     nfiundg $p |- ( ph -> F/_ y U_ x e. A B ) $=
       ( vz ciun cv wcel wrex cab df-iun nfv nfcrd nfrexdg nfabd nfcxfrd ) ACBDE
       JIKELZBDMZINBIDEOAUBCIAIPAUACBDFGACIEHQRST $.

From d45bb0f66b5ea3f2dbcd0339c506f3f92ee028da Mon Sep 17 00:00:00 2001
From: GinoGiotto <73717712+GinoGiotto@users.noreply.github.com>
Date: Mon, 1 Apr 2024 17:58:10 +0200
Subject: [PATCH 4/4] add ax12i reference

---
 set.mm | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/set.mm b/set.mm
index 2c77691fcf..7b3cdf43d0 100644
--- a/set.mm
+++ b/set.mm
@@ -21244,9 +21244,9 @@ requires either a disjoint variable condition ( ~ sb56 ) or a non-freeness
 
   $( Rederivation of axiom ~ ax-12 from ~ ax12v (used only via ~ sp ) ,
      ~ axc11r , and ~ axc15 (on top of Tarski's FOL).  Since this version
-     depends on ~ ax-13 , usage of the weaker ~ ax12v or ~ ax12w are preferred.
-     (Contributed by NM, 22-Jan-2007.)  Proof uses contemporary axioms.
-     (Revised by Wolf Lammen, 8-Aug-2020.)  (Proof shortened by BJ,
+     depends on ~ ax-13 , usage of the weaker ~ ax12v , ~ ax12w , ~ ax12i are
+     preferred.  (Contributed by NM, 22-Jan-2007.)  Proof uses contemporary
+     axioms.  (Revised by Wolf Lammen, 8-Aug-2020.)  (Proof shortened by BJ,
      4-Jul-2021.)  (New usage is discouraged.) $)
   ax12 $p |- ( x = y -> ( A. y ph -> A. x ( x = y -> ph ) ) ) $=
     ( weq wal wi axc11r ala1 syl6 a1d wn sp axc15 syl7 pm2.61i ) BCDZBEZPACEZPA