Theorem ralimia

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 19-Jul-1996)

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

Proof

Step	Hyp	Ref	Expression
1		ralimia.1	|- ( x e. A -> ( ph -> ps ) )
2	1	a2i	|- ( ( x e. A -> ph ) -> ( x e. A -> ps ) )
3	2	ralimi2	|- ( A. x e. A ph -> A. x e. A ps )