Theorem rgenw

Description: Generalization rule for restricted quantification. (Contributed by NM, 18-Jun-2014)

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

Proof

Step	Hyp	Ref	Expression
1		rgenw.1	$$⊢\phi$$
2	1	a1i	$$⊢x\in A\to \phi$$
3	2	rgen	$$⊢\forall x\in A\phi$$