Theorem cbval2vw

Description: Rule used to change bound variables, using implicit substitution. Version of cbval2vv with more disjoint variable conditions, which requires fewer axioms . (Contributed by NM, 4-Feb-2005) (Revised by Gino Giotto, 10-Jan-2024)

	Ref	Expression
Hypothesis	cbval2vw.1	|- ( ( x = z /\ y = w ) -> ( ph <-> ps ) )
Assertion	cbval2vw	|- ( A. x A. y ph <-> A. z A. w ps )

Proof

Step	Hyp	Ref	Expression
1		cbval2vw.1	|- ( ( x = z /\ y = w ) -> ( ph <-> ps ) )
2	1	cbvaldvaw	|- ( x = z -> ( A. y ph <-> A. w ps ) )
3	2	cbvalvw	|- ( A. x A. y ph <-> A. z A. w ps )