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	|- ( ph <-> ps )
Assertion	3exbii	|- ( E. x E. y E. z ph <-> E. x E. y E. z ps )

Proof

Step	Hyp	Ref	Expression
1		3exbii.1	|- ( ph <-> ps )
2	1	exbii	|- ( E. z ph <-> E. z ps )
3	2	2exbii	|- ( E. x E. y E. z ph <-> E. x E. y E. z ps )