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Theorem elabgf 2737
 Description: Membership in a class abstraction, using implicit substitution. Compare Theorem 6.13 of [Quine] p. 44. This version has bound-variable hypotheses in place of distinct variable restrictions. (Contributed by NM, 21-Sep-2003.) (Revised by Mario Carneiro, 12-Oct-2016.)
Hypotheses
Ref Expression
elabgf.1
elabgf.2
elabgf.3
Assertion
Ref Expression
elabgf

Proof of Theorem elabgf
StepHypRef Expression
1 elabgf.1 . 2
2 nfab1 2222 . . . 4
31, 2nfel 2228 . . 3
4 elabgf.2 . . 3
53, 4nfbi 1522 . 2
6 eleq1 2142 . . 3
7 elabgf.3 . . 3
86, 7bibi12d 233 . 2
9 abid 2070 . 2
101, 5, 8, 9vtoclgf 2658 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285  wnf 1390   wcel 1434  cab 2068  wnfc 2207 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:  elabf  2738  elabg  2740  elab3gf  2744  elrabf  2748  bj-intabssel  10750
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