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Theorem elabgf 2912
 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 2421 . . . 4
31, 2nfel 2427 . . 3
4 elabgf.2 . . 3
53, 4nfbi 1772 . 2
6 eleq1 2343 . . 3
7 elabgf.3 . . 3
86, 7bibi12d 312 . 2
9 abid 2271 . 2
101, 5, 8, 9vtoclgf 2842 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wnf 1531   wceq 1623   wcel 1684  cab 2269  wnfc 2406 This theorem is referenced by:  elabf  2913  elabg  2915  elab3gf  2919  elrabf  2922 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790
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