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

Theorem otex 5323
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 4525 . 2 𝐴, 𝐵, 𝐶⟩ = ⟨⟨𝐴, 𝐵⟩, 𝐶
2 opex 5322 . 2 ⟨⟨𝐴, 𝐵⟩, 𝐶⟩ ∈ V
31, 2eqeltri 2829 1 𝐴, 𝐵, 𝐶⟩ ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2114  Vcvv 3398  cop 4522  cotp 4524
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-ext 2710  ax-sep 5167  ax-nul 5174  ax-pr 5296
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-v 3400  df-dif 3846  df-un 3848  df-nul 4212  df-if 4415  df-sn 4517  df-pr 4519  df-op 4523  df-ot 4525
This theorem is referenced by:  euotd  5370  splval  14202  splcl  14203  idaval  17430  idaf  17435  eldmcoa  17437  coaval  17440  mamufval  21138  msrval  33071  msrf  33075  mapdhval  39361  mndtcco  45825
  Copyright terms: Public domain W3C validator