Theorem ralrimivv

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version with double quantification.) (Contributed by NM, 24-Jul-2004)

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

Proof

Step	Hyp	Ref	Expression
1		ralrimivv.1	|- ( ph -> ( ( x e. A /\ y e. B ) -> ps ) )
2	1	expd	|- ( ph -> ( x e. A -> ( y e. B -> ps ) ) )
3	2	ralrimdv	|- ( ph -> ( x e. A -> A. y e. B ps ) )
4	3	ralrimiv	|- ( ph -> A. x e. A A. y e. B ps )