Theorem rexbiia

Description: Inference adding restricted existential quantifier to both sides of an equivalence. (Contributed by NM, 26-Oct-1999)

	Ref	Expression
Hypothesis	rexbiia.1	|- ( x e. A -> ( ph <-> ps ) )
Assertion	rexbiia	|- ( E. x e. A ph <-> E. x e. A ps )

Proof

Step	Hyp	Ref	Expression
1		rexbiia.1	|- ( x e. A -> ( ph <-> ps ) )
2	1	pm5.32i	|- ( ( x e. A /\ ph ) <-> ( x e. A /\ ps ) )
3	2	rexbii2	|- ( E. x e. A ph <-> E. x e. A ps )