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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
StepHypRef Expression
1 rgenw.1 . . 3 φ
21a1i 10 . 2 (x Aφ)
32rgen 2679 1 x A φ
Colors of variables: wff setvar class
Syntax hints:   wcel 1710  wral 2614
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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
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