Theorem ralrimivva

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version with double quantification.) (Contributed by Jeff Madsen, 19-Jun-2011)

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

Proof

Step	Hyp	Ref	Expression
1		ralrimivva.1	|- ( ( ph /\ ( x e. A /\ y e. B ) ) -> ps )
2	1	ex	|- ( ph -> ( ( x e. A /\ y e. B ) -> ps ) )
3	2	ralrimivv	|- ( ph -> A. x e. A A. y e. B ps )