Theorem rgen

Description: Generalization rule for restricted quantification. (Contributed by NM, 19-Nov-1994)

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

Proof

Step	Hyp	Ref	Expression
1		rgen.1	$$⊢x\in A\to \phi$$
2		df-ral	$$⊢\forall x\in A\phi \leftrightarrow \forall x\left(x\in A\to \phi \right)$$
3	2 1	mpgbir	$$⊢\forall x\in A\phi$$