Theorem otex 5418

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 4576	. 2 ⊢ ⟨𝐴, 𝐵, 𝐶⟩ = ⟨⟨𝐴, 𝐵⟩, 𝐶⟩
2		opex 5416	. 2 ⊢ ⟨⟨𝐴, 𝐵⟩, 𝐶⟩ ∈ V
3	1, 2	eqeltri 2832	1 ⊢ ⟨𝐴, 𝐵, 𝐶⟩ ∈ V

Syntax hints:   ∈ wcel 2114  Vcvv 3429  ⟨cop 4573  ⟨cotp 4575

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708  ax-sep 5231  ax-pr 5375

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-rab 3390  df-v 3431  df-un 3894  df-in 3896  df-ss 3906  df-sn 4568  df-pr 4570  df-op 4574  df-ot 4576

This theorem is referenced by:  euotd  5467  ralxp3f  8087  xpord3lem  8099  xpord3pred  8102  splval  14713  splcl  14714  idaval  18025  idaf  18030  eldmcoa  18032  coaval  18035  mamufval  22357  msrval  35720  msrf  35724  mapdhval  42170  mndtcco  50060