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

Theorem otth 4432
 Description: Ordered triple theorem. (Contributed by NM, 25-Sep-2014.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypotheses
Ref Expression
otth.1
otth.2
otth.3
Assertion
Ref Expression
otth

Proof of Theorem otth
StepHypRef Expression
1 df-ot 3816 . . 3
2 df-ot 3816 . . 3
31, 2eqeq12i 2448 . 2
4 otth.1 . . 3
5 otth.2 . . 3
6 otth.3 . . 3
74, 5, 6otth2 4431 . 2
83, 7bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   w3a 936   wceq 1652   wcel 1725  cvv 2948  cop 3809  cotp 3810 This theorem is referenced by:  euotd  4449  2spotiundisj  28388 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-ot 3816
 Copyright terms: Public domain W3C validator