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Theorem opid 3558
Description: The ordered pair  <. ,  >. in Kuratowski's representation. (Contributed by FL, 28-Dec-2011.)
Hypothesis
Ref Expression
opid.1  _V
Assertion
Ref Expression
opid  <. ,  >.  { { } }

Proof of Theorem opid
StepHypRef Expression
1 dfsn2 3381 . . . 4  { }  { ,  }
21eqcomi 2041 . . 3  { ,  }  { }
32preq2i 3442 . 2  { { } ,  { ,  } }  { { } ,  { } }
4 opid.1 . . 3  _V
54, 4dfop 3539 . 2  <. ,  >.  { { } ,  { ,  } }
6 dfsn2 3381 . 2  { { } }  { { } ,  { } }
73, 5, 63eqtr4i 2067 1  <. ,  >.  { { } }
Colors of variables: wff set class
Syntax hints:   wceq 1242   wcel 1390   _Vcvv 2551   {csn 3367   {cpr 3368   <.cop 3370
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376
This theorem is referenced by:  dmsnsnsng  4741  funopg  4877
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