Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  opthg2 Unicode version

Theorem opthg2 4140
 Description: Ordered pair theorem. (Contributed by NM, 14-Oct-2005.) (Revised by Mario Carneiro, 26-Apr-2015.)
Assertion
Ref Expression
opthg2

Proof of Theorem opthg2
StepHypRef Expression
1 opthg 4139 . 2
2 eqcom 2255 . 2
3 eqcom 2255 . . 3
4 eqcom 2255 . . 3
53, 4anbi12i 681 . 2
61, 2, 53bitr4g 281 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360   wceq 1619   wcel 1621  cop 3547 This theorem is referenced by:  opth2  4141  fliftel  5660 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553
 Copyright terms: Public domain W3C validator