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

Theorem otex 5356
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 4575 . 2 𝐴, 𝐵, 𝐶⟩ = ⟨⟨𝐴, 𝐵⟩, 𝐶
2 opex 5355 . 2 ⟨⟨𝐴, 𝐵⟩, 𝐶⟩ ∈ V
31, 2eqeltri 2909 1 𝐴, 𝐵, 𝐶⟩ ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2110  Vcvv 3494  cop 4572  cotp 4574
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2157  ax-12 2173  ax-ext 2793  ax-sep 5202  ax-nul 5209  ax-pr 5329
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1536  df-ex 1777  df-nf 1781  df-sb 2066  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-v 3496  df-dif 3938  df-un 3940  df-in 3942  df-ss 3951  df-nul 4291  df-if 4467  df-sn 4567  df-pr 4569  df-op 4573  df-ot 4575
This theorem is referenced by:  euotd  5402  splval  14112  splcl  14113  idaval  17317  idaf  17322  eldmcoa  17324  coaval  17327  mamufval  20995  msrval  32785  msrf  32789  mapdhval  38859
  Copyright terms: Public domain W3C validator