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Theorem brtpid1 25178
Description: A binary relationship 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 4427 . . 3  |-  <. A ,  B >.  e.  _V
21tpid1 3917 . 2  |-  <. A ,  B >.  e.  { <. A ,  B >. ,  C ,  D }
3 df-br 4213 . 2  |-  ( A { <. A ,  B >. ,  C ,  D } B  <->  <. A ,  B >.  e.  { <. A ,  B >. ,  C ,  D } )
42, 3mpbir 201 1  |-  A { <. A ,  B >. ,  C ,  D } B
Colors of variables: wff set class
Syntax hints:    e. wcel 1725   {ctp 3816   <.cop 3817   class class class wbr 4212
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-tp 3822  df-op 3823  df-br 4213
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