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Theorem brtpid2 30347
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 4663 . . 3  |-  <. A ,  B >.  e.  _V
21tpid2 4085 . 2  |-  <. A ,  B >.  e.  { C ,  <. A ,  B >. ,  D }
3 df-br 4402 . 2  |-  ( A { C ,  <. A ,  B >. ,  D } B  <->  <. A ,  B >.  e.  { C ,  <. A ,  B >. ,  D } )
42, 3mpbir 213 1  |-  A { C ,  <. A ,  B >. ,  D } B
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1886   {ctp 3971   <.cop 3973   class class class wbr 4401
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-9 1895  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430  ax-sep 4524  ax-nul 4533  ax-pr 4638
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3or 985  df-3an 986  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ne 2623  df-v 3046  df-dif 3406  df-un 3408  df-in 3410  df-ss 3417  df-nul 3731  df-if 3881  df-sn 3968  df-pr 3970  df-tp 3972  df-op 3974  df-br 4402
This theorem is referenced by: (None)
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