Theorem cbvreuvw

Description: Change the bound variable of a restricted unique existential quantifier using implicit substitution. Version of cbvreuv with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 5-Apr-2004) (Revised by Gino Giotto, 10-Jan-2024)

	Ref	Expression
Hypothesis	cbvralvw.1	|- ( x = y -> ( ph <-> ps ) )
Assertion	cbvreuvw	|- ( E! x e. A ph <-> E! y e. A ps )

Proof

Step	Hyp	Ref	Expression
1		cbvralvw.1	|- ( x = y -> ( ph <-> ps ) )
2		nfv	|- F/ y ph
3		nfv	|- F/ x ps
4	2 3 1	cbvreuw	|- ( E! x e. A ph <-> E! y e. A ps )