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Theorem brtpid1 32958
 Description: A binary relation involving unordered triplets. (Contributed by Scott Fenton, 7-Jun-2016.)
Assertion
Ref Expression
brtpid1 𝐴{⟨𝐴, 𝐵⟩, 𝐶, 𝐷}𝐵

Proof of Theorem brtpid1
StepHypRef Expression
1 opex 5329 . . 3 𝐴, 𝐵⟩ ∈ V
21tpid1 4677 . 2 𝐴, 𝐵⟩ ∈ {⟨𝐴, 𝐵⟩, 𝐶, 𝐷}
3 df-br 5040 . 2 (𝐴{⟨𝐴, 𝐵⟩, 𝐶, 𝐷}𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ {⟨𝐴, 𝐵⟩, 𝐶, 𝐷})
42, 3mpbir 234 1 𝐴{⟨𝐴, 𝐵⟩, 𝐶, 𝐷}𝐵
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2115  {ctp 4544  ⟨cop 4546   class class class wbr 5039 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 2178  ax-ext 2793  ax-sep 5176  ax-nul 5183  ax-pr 5303 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 2800  df-cleq 2814  df-clel 2892  df-nfc 2960  df-v 3473  df-dif 3913  df-un 3915  df-in 3917  df-ss 3927  df-nul 4267  df-if 4441  df-sn 4541  df-pr 4543  df-tp 4545  df-op 4547  df-br 5040 This theorem is referenced by: (None)
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