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	⊢ ∀ 𝑥 ∈ 𝐴 ∀ 𝑦 ∈ 𝐵 𝜑

Proof

Step	Hyp	Ref	Expression
1		rgenw.1	⊢ 𝜑
2	1	rgenw	⊢ ∀ 𝑦 ∈ 𝐵 𝜑
3	2	rgenw	⊢ ∀ 𝑥 ∈ 𝐴 ∀ 𝑦 ∈ 𝐵 𝜑