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Theorem brtpid2 33188
 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 5327 . . 3 𝐴, 𝐵⟩ ∈ V
21tpid2 4666 . 2 𝐴, 𝐵⟩ ∈ {𝐶, ⟨𝐴, 𝐵⟩, 𝐷}
3 df-br 5036 . 2 (𝐴{𝐶, ⟨𝐴, 𝐵⟩, 𝐷}𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ {𝐶, ⟨𝐴, 𝐵⟩, 𝐷})
42, 3mpbir 234 1 𝐴{𝐶, ⟨𝐴, 𝐵⟩, 𝐷}𝐵
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2111  {ctp 4529  ⟨cop 4531   class class class wbr 5035 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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2729  ax-sep 5172  ax-nul 5179  ax-pr 5301 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3or 1085  df-3an 1086  df-tru 1541  df-fal 1551  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-v 3411  df-dif 3863  df-un 3865  df-nul 4228  df-if 4424  df-sn 4526  df-pr 4528  df-tp 4530  df-op 4532  df-br 5036 This theorem is referenced by: (None)
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