Theorem wl-rgen

Description: Generalization rule for restricted quantification. (Contributed by Wolf Lammen, 10-Jun-2023)

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

Proof

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