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Metamath Proof Explorer

Theorem rgen

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

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

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