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	$$⊢\phi \leftrightarrow \psi$$
Assertion	2rexbii	$$⊢\exists x\in A\exists y\in B\phi \leftrightarrow \exists x\in A\exists y\in B\psi$$

Proof

Step	Hyp	Ref	Expression
1		2rexbii.1	$$⊢\phi \leftrightarrow \psi$$
2	1	rexbii	$$⊢\exists y\in B\phi \leftrightarrow \exists y\in B\psi$$
3	2	rexbii	$$⊢\exists x\in A\exists y\in B\phi \leftrightarrow \exists x\in A\exists y\in B\psi$$