Theorem 2rexbii

Description: Inference adding two restricted existential quantifiers to both sides of an equivalence. (Contributed by NM, 11-Nov-1995)

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

Proof

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