Theorem cbvalv

Description: 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) (New usage is discouraged.)

	Ref	Expression
Hypothesis	cbvalv.1	|- ( x = y -> ( ph <-> ps ) )
Assertion	cbvalv	|- ( A. x ph <-> A. y ps )

Proof

Step	Hyp	Ref	Expression
1		cbvalv.1	|- ( x = y -> ( ph <-> ps ) )
2		nfv	|- F/ y ph
3		nfv	|- F/ x ps
4	2 3 1	cbval	|- ( A. x ph <-> A. y ps )