Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  abid2f Unicode version

Theorem abid2f 2648
 Description: A simplification of class abstraction. Theorem 5.2 of [Quine] p. 35. (Contributed by NM, 5-Sep-2011.) (Revised by Mario Carneiro, 7-Oct-2016.) (Proof shortened by Wolf Lammen, 17-Nov-2019.)
Hypothesis
Ref Expression
abid2f.1
Assertion
Ref Expression
abid2f

Proof of Theorem abid2f
StepHypRef Expression
1 nfab1 2621 . . 3
2 abid2f.1 . . 3
31, 2cleqf 2646 . 2
4 abid 2444 . 2
53, 4mpgbir 1622 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  =wceq 1395  e.wcel 1818  {cab 2442  F/_wnfc 2605 This theorem is referenced by:  mptctf  27544  rabexgf  31399 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-or 370  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
 Copyright terms: Public domain W3C validator