Theorem ralimi

Description: Inference quantifying both antecedent and consequent, with strong hypothesis. (Contributed by NM, 4-Mar-1997)

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

Proof

Step	Hyp	Ref	Expression
1		ralimi.1	|- ( ph -> ps )
2	1	a1i	|- ( x e. A -> ( ph -> ps ) )
3	2	ralimia	|- ( A. x e. A ph -> A. x e. A ps )