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Theorem rgen3 2895
 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 1188 . . 3
32ralrimiva 2881 . 2
43rgen2 2894 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   w3a 965   wcel 1757  wral 2792 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1709  ax-7 1729  ax-12 1793 This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 967  df-ex 1588  df-nf 1591  df-ral 2797 This theorem is referenced by:  isposi  15214  addcnlem  20542  isgrpoi  23806  cnrngo  24011  lnocoi  24278  0lnfn  25510  lnopcoi  25528  xrge0omnd  26294  reofld  26428  signswmnd  27078  poseq  27834
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