Theorem rgenw 2681

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

Hypothesis

Ref	Expression
rgenw.1	|- ph

Assertion

Ref	Expression
rgenw	|- A.x e. A ph

Proof of Theorem rgenw

Step	Hyp	Ref	Expression
1		rgenw.1	. . 3 |- ph
2	1	a1i 10	. 2 |- (x e. A -> ph)
3	2	rgen 2679	1 |- A.x e. A ph

Syntax hints:   e. wcel 1710  A.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