Theorem cbvreuv

Description: Change the bound variable of a restricted unique existential quantifier using implicit substitution. See cbvreuvw for a version without ax-13 , but extra disjoint variables. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker cbvreuvw when possible. (Contributed by NM, 5-Apr-2004) (Revised by Mario Carneiro, 15-Oct-2016) (New usage is discouraged.)

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

Proof

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