Theorem 3exbii

Description: Inference adding three existential quantifiers to both sides of an equivalence. (Contributed by NM, 2-May-1995)

	Ref	Expression
Hypothesis	3exbii.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	3exbii	$$⊢\exists x\exists y\exists z\phi \leftrightarrow \exists x\exists y\exists z\psi$$

Proof

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