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Theorem brtpid2 24091
Description: A binary relationship involving unordered triplets. (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 4253 . . 3  |-  <. A ,  B >.  e.  _V
21tpid2 3753 . 2  |-  <. A ,  B >.  e.  { C ,  <. A ,  B >. ,  D }
3 df-br 4040 . 2  |-  ( A { C ,  <. A ,  B >. ,  D } B  <->  <. A ,  B >.  e.  { C ,  <. A ,  B >. ,  D } )
42, 3mpbir 200 1  |-  A { C ,  <. A ,  B >. ,  D } B
Colors of variables: wff set class
Syntax hints:    e. wcel 1696   {ctp 3655   <.cop 3656   class class class wbr 4039
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-tp 3661  df-op 3662  df-br 4040
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