Theorem reximia

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 10-Feb-1997)

	Ref	Expression
Hypothesis	reximia.1	|- ( x e. A -> ( ph -> ps ) )
Assertion	reximia	|- ( E. x e. A ph -> E. x e. A ps )

Proof

Step	Hyp	Ref	Expression
1		reximia.1	|- ( x e. A -> ( ph -> ps ) )
2		rexim	|- ( A. x e. A ( ph -> ps ) -> ( E. x e. A ph -> E. x e. A ps ) )
3	2 1	mprg	|- ( E. x e. A ph -> E. x e. A ps )