Theorem ralimiaa

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 4-Aug-2007)

	Ref	Expression
Hypothesis	ralimiaa.1	|- ( ( x e. A /\ ph ) -> ps )
Assertion	ralimiaa	|- ( A. x e. A ph -> A. x e. A ps )

Proof

Step	Hyp	Ref	Expression
1		ralimiaa.1	|- ( ( x e. A /\ ph ) -> ps )
2	1	ex	|- ( x e. A -> ( ph -> ps ) )
3	2	ralimia	|- ( A. x e. A ph -> A. x e. A ps )