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Theorem rgen3 2803
 Description: Generalization rule for restricted quantification. (Contributed by NM, 12-Jan-2008.)
Hypothesis
Ref Expression
rgen3.1
Assertion
Ref Expression
rgen3
Distinct variable groups:   ,,   ,   ,,
Allowed substitution hints:   (,,)   ()   (,)   (,,)

Proof of Theorem rgen3
StepHypRef Expression
1 rgen3.1 . . . 4
213expa 1153 . . 3
32ralrimiva 2789 . 2
43rgen2 2802 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   w3a 936   wcel 1725  wral 2705 This theorem is referenced by:  isposi  14413  addcnlem  18894  isgrpoi  21786  cnrngo  21991  lnocoi  22258  0lnfn  23488  lnopcoi  23506  poseq  25528  modprm0g  28229 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-an 361  df-3an 938  df-ex 1551  df-nf 1554  df-ral 2710
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