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Theorem elabgf 3230
 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 2607 . . . 4
31, 2nfel 2618 . . 3
4 elabgf.2 . . 3
53, 4nfbi 1920 . 2
6 eleq1 2515 . . 3
7 elabgf.3 . . 3
86, 7bibi12d 321 . 2
9 abid 2430 . 2
101, 5, 8, 9vtoclgf 3151 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wceq 1383  wnf 1603   wcel 1804  cab 2428  wnfc 2591 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-v 3097 This theorem is referenced by:  elabf  3231  elabg  3233  elab3gf  3237  elrabf  3241
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