Theorem 2exbii

Description: Inference adding two existential quantifiers to both sides of an equivalence. (Contributed by NM, 16-Mar-1995)

	Ref	Expression
Hypothesis	2exbii.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	2exbii	$$⊢\exists x\exists y\phi \leftrightarrow \exists x\exists y\psi$$

Proof

Step	Hyp	Ref	Expression
1		2exbii.1	$$⊢\phi \leftrightarrow \psi$$
2	1	exbii	$$⊢\exists y\phi \leftrightarrow \exists y\psi$$
3	2	exbii	$$⊢\exists x\exists y\phi \leftrightarrow \exists x\exists y\psi$$