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Theorem opid 3567
 Description: The ordered pair in Kuratowski's representation. (Contributed by FL, 28-Dec-2011.)
Hypothesis
Ref Expression
opid.1
Assertion
Ref Expression
opid

Proof of Theorem opid
StepHypRef Expression
1 dfsn2 3389 . . . 4
21eqcomi 2044 . . 3
32preq2i 3451 . 2
4 opid.1 . . 3
54, 4dfop 3548 . 2
6 dfsn2 3389 . 2
73, 5, 63eqtr4i 2070 1
 Colors of variables: wff set class Syntax hints:   wceq 1243   wcel 1393  cvv 2557  csn 3375  cpr 3376  cop 3378 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384 This theorem is referenced by:  dmsnsnsng  4798  funopg  4934
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