Theorem rgen2w

Description: Generalization rule for restricted quantification. Note that x and y needn't be distinct. (Contributed by NM, 18-Jun-2014)

	Ref	Expression
Hypothesis	rgenw.1	$$⊢\phi$$
Assertion	rgen2w	$$⊢\forall x\in A\forall y\in B\phi$$

Proof

Step	Hyp	Ref	Expression
1		rgenw.1	$$⊢\phi$$
2	1	rgenw	$$⊢\forall y\in B\phi$$
3	2	rgenw	$$⊢\forall x\in A\forall y\in B\phi$$