Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  otth2 Structured version   Unicode version

Theorem otth2 4474
 Description: Ordered triple theorem, with triple express with ordered pairs. (Contributed by NM, 1-May-1995.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypotheses
Ref Expression
otth.1
otth.2
otth.3
Assertion
Ref Expression
otth2

Proof of Theorem otth2
StepHypRef Expression
1 otth.1 . . . 4
2 otth.2 . . . 4
31, 2opth 4470 . . 3
43anbi1i 678 . 2
5 opex 4462 . . 3
6 otth.3 . . 3
75, 6opth 4470 . 2
8 df-3an 939 . 2
94, 7, 83bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   w3a 937   wceq 1654   wcel 1728  cvv 2965  cop 3846 This theorem is referenced by:  otth  4475  oprabid  6141  eloprabga  6196 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-14 1732  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424  ax-sep 4361  ax-nul 4369  ax-pr 4438 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-rab 2721  df-v 2967  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3768  df-sn 3849  df-pr 3850  df-op 3852
 Copyright terms: Public domain W3C validator