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Theorem elabgf 2849
 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 2387 . . . 4
31, 2nfel 2393 . . 3
4 elabgf.2 . . 3
53, 4nfbi 1738 . 2
6 eleq1 2313 . . 3
7 elabgf.3 . . 3
86, 7bibi12d 314 . 2
9 abid 2241 . 2
101, 5, 8, 9vtoclgf 2780 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178  wnf 1539   wceq 1619   wcel 1621  cab 2239  wnfc 2372 This theorem is referenced by:  elabf  2850  elabg  2852  elab3gf  2856  elrabf  2859 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729
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