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Metamath Proof Explorer

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	$⊢ φ$
	Assertion	rgen2w	$⊢ \forall x \in A \forall y \in B φ$

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