Theorem cbval2vv

Description: 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.)

	Ref	Expression
Hypothesis	cbval2vv.1	|- ( ( x = z /\ y = w ) -> ( ph <-> ps ) )
Assertion	cbval2vv	|- ( A. x A. y ph <-> A. z A. w ps )

Proof

Step	Hyp	Ref	Expression
1		cbval2vv.1	|- ( ( x = z /\ y = w ) -> ( ph <-> ps ) )
2	1	cbvaldva	|- ( x = z -> ( A. y ph <-> A. w ps ) )
3	2	cbvalv	|- ( A. x A. y ph <-> A. z A. w ps )