Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  brtpid1 Structured version   Visualization version   GIF version

Theorem brtpid1 31921
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 5119 . . 3 𝐴, 𝐵⟩ ∈ V
21tpid1 4491 . 2 𝐴, 𝐵⟩ ∈ {⟨𝐴, 𝐵⟩, 𝐶, 𝐷}
3 df-br 4841 . 2 (𝐴{⟨𝐴, 𝐵⟩, 𝐶, 𝐷}𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ {⟨𝐴, 𝐵⟩, 𝐶, 𝐷})
42, 3mpbir 222 1 𝐴{⟨𝐴, 𝐵⟩, 𝐶, 𝐷}𝐵
Colors of variables: wff setvar class
Syntax hints:  wcel 2158  {ctp 4371  cop 4373   class class class wbr 4840
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1880  ax-4 1897  ax-5 2004  ax-6 2070  ax-7 2106  ax-9 2167  ax-10 2187  ax-11 2203  ax-12 2216  ax-13 2422  ax-ext 2784  ax-sep 4971  ax-nul 4980  ax-pr 5093
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-3or 1101  df-3an 1102  df-tru 1641  df-ex 1860  df-nf 1865  df-sb 2063  df-clab 2792  df-cleq 2798  df-clel 2801  df-nfc 2936  df-v 3392  df-dif 3769  df-un 3771  df-in 3773  df-ss 3780  df-nul 4114  df-if 4277  df-sn 4368  df-pr 4370  df-tp 4372  df-op 4374  df-br 4841
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator