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Theorem elabg 2740
 Description: Membership in a class abstraction, using implicit substitution. Compare Theorem 6.13 of [Quine] p. 44. (Contributed by NM, 14-Apr-1995.)
Hypothesis
Ref Expression
elabg.1
Assertion
Ref Expression
elabg
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem elabg
StepHypRef Expression
1 nfcv 2220 . 2
2 nfv 1462 . 2
3 elabg.1 . 2
41, 2, 3elabgf 2737 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285   wcel 1434  cab 2068 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604 This theorem is referenced by:  elab2g  2741  intmin3  3671  finds  4349  elxpi  4387  ovelrn  5680  indpi  6594  peano5nnnn  7120  peano5nni  8109
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