Theorem exbii

Description: Inference adding existential quantifier to both sides of an equivalence. (Contributed by NM, 24-May-1994)

	Ref	Expression
Hypothesis	exbii.1	|- ( ph <-> ps )
Assertion	exbii	|- ( E. x ph <-> E. x ps )

Proof

Step	Hyp	Ref	Expression
1		exbii.1	|- ( ph <-> ps )
2		exbi	|- ( A. x ( ph <-> ps ) -> ( E. x ph <-> E. x ps ) )
3	2 1	mpg	|- ( E. x ph <-> E. x ps )