Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  otex Structured version   Visualization version   GIF version

Theorem otex 4894
 Description: An ordered triple of classes is a set. (Contributed by NM, 3-Apr-2015.)
Assertion
Ref Expression
otex 𝐴, 𝐵, 𝐶⟩ ∈ V

Proof of Theorem otex
StepHypRef Expression
1 df-ot 4157 . 2 𝐴, 𝐵, 𝐶⟩ = ⟨⟨𝐴, 𝐵⟩, 𝐶
2 opex 4893 . 2 ⟨⟨𝐴, 𝐵⟩, 𝐶⟩ ∈ V
31, 2eqeltri 2694 1 𝐴, 𝐵, 𝐶⟩ ∈ V
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1987  Vcvv 3186  ⟨cop 4154  ⟨cotp 4156 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4741  ax-nul 4749  ax-pr 4867 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3188  df-dif 3558  df-un 3560  df-in 3562  df-ss 3569  df-nul 3892  df-if 4059  df-sn 4149  df-pr 4151  df-op 4155  df-ot 4157 This theorem is referenced by:  euotd  4935  splval  13439  splcl  13440  idaval  16629  idaf  16634  eldmcoa  16636  coaval  16639  mamufval  20110  msrval  31140  msrf  31144  mapdhval  36490
 Copyright terms: Public domain W3C validator