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janitorial work: add references to similar theorems (#3797)
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wlammen authored Jan 27, 2024
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Expand Up @@ -27222,7 +27222,8 @@ 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 ).
$( Substitution applied to an atomic wff (class version of ~ elsb3 ). 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.) $)
Expand Down Expand Up @@ -31321,18 +31322,21 @@ Such interpretation is rarely needed (see also ~ df-ral ). (Contributed
$d x A $. $d y A $. $d y ph $. $d x ps $.
cbvralv.1 $e |- ( x = y -> ( ph <-> ps ) ) $.
$( Change the bound variable of a restricted universal quantifier using
implicit substitution. (Contributed by NM, 28-Jan-1997.) $)
implicit substitution. See ~ cbvralvw based on fewer axioms , but extra
disjoint variables. (Contributed by NM, 28-Jan-1997.) $)
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. (Contributed by NM, 2-Jun-1998.) $)
implicit substitution. See ~ cbvrexvw based on fewer axioms , but extra
disjoint variables. (Contributed by NM, 2-Jun-1998.) $)
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. (Contributed by NM, 5-Apr-2004.) (Revised
by Mario Carneiro, 15-Oct-2016.) $)
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.) $)
cbvreuv $p |- ( E! x e. A ph <-> E! y e. A ps ) $=
( nfv cbvreu ) ABCDEADGBCGFH $.

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