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Theorem elabgf 3080
 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 2574 . . . 4
31, 2nfel 2580 . . 3
4 elabgf.2 . . 3
53, 4nfbi 1856 . 2
6 eleq1 2496 . . 3
7 elabgf.3 . . 3
86, 7bibi12d 313 . 2
9 abid 2424 . 2
101, 5, 8, 9vtoclgf 3010 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wnf 1553   wceq 1652   wcel 1725  cab 2422  wnfc 2559 This theorem is referenced by:  elabf  3081  elabg  3083  elab3gf  3087  elrabf  3091 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958
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