Theorem 2rexbiia

Description: Inference adding two restricted existential quantifiers to both sides of an equivalence. (Contributed by NM, 1-Aug-2004)

	Ref	Expression
Hypothesis	2rexbiia.1	|- ( ( x e. A /\ y e. B ) -> ( ph <-> ps ) )
Assertion	2rexbiia	|- ( E. x e. A E. y e. B ph <-> E. x e. A E. y e. B ps )

Proof

Step	Hyp	Ref	Expression
1		2rexbiia.1	|- ( ( x e. A /\ y e. B ) -> ( ph <-> ps ) )
2	1	rexbidva	|- ( x e. A -> ( E. y e. B ph <-> E. y e. B ps ) )
3	2	rexbiia	|- ( E. x e. A E. y e. B ph <-> E. x e. A E. y e. B ps )