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Theorem rgenw 2681

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

**Hypothesis**
Ref	Expression
rgenw.1	⊢ φ

**Assertion**
Ref	Expression
rgenw	⊢ ∀x ∈ A φ

**Proof of Theorem rgenw**
Step	Hyp	Ref	Expression
1		rgenw.1	. . 3 ⊢ φ
2	1	a1i 10	. 2 ⊢ (x ∈ A → φ)
3	2	rgen 2679	1 ⊢ ∀x ∈ A φ

Colors of variables: wff setvar class

Syntax hints: ∈ wcel 1710 ∀wral 2614

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546

This theorem depends on definitions: df-bi 177 df-ral 2619

This theorem is referenced by: rgen2w 2682 reuun1 3537 riinrab 4041 evenodddisj 4516 vfinspnn 4541 mpt2eq12 5662 fnmpti 5690 clos10 5887 fnpm 6008 frecxp 6314