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

Theorem abid2f 2444
 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.)
Hypothesis
Ref Expression
abid2f.1
Assertion
Ref Expression
abid2f

Proof of Theorem abid2f
StepHypRef Expression
1 abid2f.1 . . . . 5
2 nfab1 2421 . . . . 5
31, 2cleqf 2443 . . . 4
4 abid 2271 . . . . . 6
54bibi2i 304 . . . . 5
65albii 1553 . . . 4
73, 6bitri 240 . . 3
8 biid 227 . . 3
97, 8mpgbir 1537 . 2
109eqcomi 2287 1
 Colors of variables: wff set class Syntax hints:   wb 176  wal 1527   wceq 1623   wcel 1684  cab 2269  wnfc 2406 This theorem is referenced by:  mptctf  23348  rabexgf  27695 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
 Copyright terms: Public domain W3C validator