Theorem otex 5374

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

Step	Hyp	Ref	Expression
1		df-ot 4567	. 2 ⊢ ⟨𝐴, 𝐵, 𝐶⟩ = ⟨⟨𝐴, 𝐵⟩, 𝐶⟩
2		opex 5373	. 2 ⊢ ⟨⟨𝐴, 𝐵⟩, 𝐶⟩ ∈ V
3	1, 2	eqeltri 2835	1 ⊢ ⟨𝐴, 𝐵, 𝐶⟩ ∈ V

Syntax hints:   ∈ wcel 2108  Vcvv 3422  ⟨cop 4564  ⟨cotp 4566

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709  ax-sep 5218  ax-nul 5225  ax-pr 5347

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-3an 1087  df-tru 1542  df-fal 1552  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-dif 3886  df-un 3888  df-nul 4254  df-if 4457  df-sn 4559  df-pr 4561  df-op 4565  df-ot 4567

This theorem is referenced by:  euotd  5421  splval  14392  splcl  14393  idaval  17689  idaf  17694  eldmcoa  17696  coaval  17699  mamufval  21444  msrval  33400  msrf  33404  mapdhval  39665  mndtcco  46258