Theorem ralrimiva

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 2-Jan-2006)

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

Proof

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