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Theorem brtpid3 33010
 Description: A binary relation involving unordered triples. (Contributed by Scott Fenton, 7-Jun-2016.)
Assertion
Ref Expression
brtpid3 𝐴{𝐶, 𝐷, ⟨𝐴, 𝐵⟩}𝐵

Proof of Theorem brtpid3
StepHypRef Expression
1 opex 5343 . . 3 𝐴, 𝐵⟩ ∈ V
21tpid3 4694 . 2 𝐴, 𝐵⟩ ∈ {𝐶, 𝐷, ⟨𝐴, 𝐵⟩}
3 df-br 5053 . 2 (𝐴{𝐶, 𝐷, ⟨𝐴, 𝐵⟩}𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ {𝐶, 𝐷, ⟨𝐴, 𝐵⟩})
42, 3mpbir 234 1 𝐴{𝐶, 𝐷, ⟨𝐴, 𝐵⟩}𝐵
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2115  {ctp 4554  ⟨cop 4556   class class class wbr 5052 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 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5189  ax-nul 5196  ax-pr 5317 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3or 1085  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-v 3482  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4277  df-if 4451  df-sn 4551  df-pr 4553  df-tp 4555  df-op 4557  df-br 5053 This theorem is referenced by: (None)
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