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Theorem brtpid2 35224
Description: A binary relation involving unordered triples. (Contributed by Scott Fenton, 7-Jun-2016.)
Assertion
Ref Expression
brtpid2 𝐴{𝐶, ⟨𝐴, 𝐵⟩, 𝐷}𝐵

Proof of Theorem brtpid2
StepHypRef Expression
1 opex 5457 . . 3 𝐴, 𝐵⟩ ∈ V
21tpid2 4769 . 2 𝐴, 𝐵⟩ ∈ {𝐶, ⟨𝐴, 𝐵⟩, 𝐷}
3 df-br 5142 . 2 (𝐴{𝐶, ⟨𝐴, 𝐵⟩, 𝐷}𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ {𝐶, ⟨𝐴, 𝐵⟩, 𝐷})
42, 3mpbir 230 1 𝐴{𝐶, ⟨𝐴, 𝐵⟩, 𝐷}𝐵
Colors of variables: wff setvar class
Syntax hints:  wcel 2098  {ctp 4627  cop 4629   class class class wbr 5141
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697  ax-sep 5292  ax-nul 5299  ax-pr 5420
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3or 1085  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-tp 4628  df-op 4630  df-br 5142
This theorem is referenced by: (None)
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