Theorem cbvex2vw

Description: Rule used to change bound variables, using implicit substitution. Version of cbvex2vv with more disjoint variable conditions, which requires fewer axioms . (Contributed by NM, 26-Jul-1995) (Revised by Gino Giotto, 10-Jan-2024)

	Ref	Expression
Hypothesis	cbval2vw.1	|- ( ( x = z /\ y = w ) -> ( ph <-> ps ) )
Assertion	cbvex2vw	|- ( E. x E. y ph <-> E. z E. w ps )

Proof

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