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Theorem brtpid3 25181
Description: A binary relationship involving unordered triplets. (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 4428 . . 3  |-  <. A ,  B >.  e.  _V
21tpid3 3921 . 2  |-  <. A ,  B >.  e.  { C ,  D ,  <. A ,  B >. }
3 df-br 4214 . 2  |-  ( A { C ,  D ,  <. A ,  B >. } B  <->  <. A ,  B >.  e.  { C ,  D ,  <. A ,  B >. } )
42, 3mpbir 202 1  |-  A { C ,  D ,  <. A ,  B >. } B
Colors of variables: wff set class
Syntax hints:    e. wcel 1726   {ctp 3817   <.cop 3818   class class class wbr 4213
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-tp 3823  df-op 3824  df-br 4214
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