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

Theorem otex 5476
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 4640 . 2 𝐴, 𝐵, 𝐶⟩ = ⟨⟨𝐴, 𝐵⟩, 𝐶
2 opex 5475 . 2 ⟨⟨𝐴, 𝐵⟩, 𝐶⟩ ∈ V
31, 2eqeltri 2835 1 𝐴, 𝐵, 𝐶⟩ ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2106  Vcvv 3478  cop 4637  cotp 4639
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 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-ot 4640
This theorem is referenced by:  euotd  5523  ralxp3f  8161  xpord3lem  8173  xpord3pred  8176  splval  14786  splcl  14787  idaval  18112  idaf  18117  eldmcoa  18119  coaval  18122  mamufval  22412  msrval  35523  msrf  35527  mapdhval  41707  mndtcco  48894
  Copyright terms: Public domain W3C validator