Theorem rgen2

Description: Generalization rule for restricted quantification, with two quantifiers. This theorem should be used in place of rgen2a since it depends on a smaller set of axioms. (Contributed by NM, 30-May-1999)

	Ref	Expression
Hypothesis	rgen2.1	|- ( ( x e. A /\ y e. B ) -> ph )
Assertion	rgen2	|- A. x e. A A. y e. B ph

Proof

Step	Hyp	Ref	Expression
1		rgen2.1	|- ( ( x e. A /\ y e. B ) -> ph )
2	1	ralrimiva	|- ( x e. A -> A. y e. B ph )
3	2	rgen	|- A. x e. A A. y e. B ph