Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  brtpid2 Structured version   Visualization version   GIF version

Theorem brtpid2 35676
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 5487 . . 3 𝐴, 𝐵⟩ ∈ V
21tpid2 4795 . 2 𝐴, 𝐵⟩ ∈ {𝐶, ⟨𝐴, 𝐵⟩, 𝐷}
3 df-br 5170 . 2 (𝐴{𝐶, ⟨𝐴, 𝐵⟩, 𝐷}𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ {𝐶, ⟨𝐴, 𝐵⟩, 𝐷})
42, 3mpbir 231 1 𝐴{𝐶, ⟨𝐴, 𝐵⟩, 𝐷}𝐵
Colors of variables: wff setvar class
Syntax hints:  wcel 2103  {ctp 4652  cop 4654   class class class wbr 5169
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2105  ax-9 2113  ax-ext 2705  ax-sep 5320  ax-nul 5327  ax-pr 5450
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3or 1088  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2712  df-cleq 2726  df-clel 2813  df-v 3484  df-dif 3973  df-un 3975  df-ss 3987  df-nul 4348  df-if 4549  df-sn 4649  df-pr 4651  df-tp 4653  df-op 4655  df-br 5170
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator