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Theorem elabgf 3244
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 2621 . . . 4
31, 2nfel 2632 . . 3
4 elabgf.2 . . 3
53, 4nfbi 1934 . 2
6 eleq1 2529 . . 3
7 elabgf.3 . . 3
86, 7bibi12d 321 . 2
9 abid 2444 . 2
101, 5, 8, 9vtoclgf 3165 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  F/wnf 1616  e.wcel 1818  {cab 2442  F/_wnfc 2605
This theorem is referenced by:  elabf  3245  elabg  3247  elab3gf  3251  elrabf  3255
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111
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