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Theorem opid 4236
Description: The ordered pair in Kuratowski's representation. (Contributed by FL, 28-Dec-2011.) (Avoid depending on this detail.)
Hypothesis
Ref Expression
opid.1
Assertion
Ref Expression
opid

Proof of Theorem opid
StepHypRef Expression
1 dfsn2 4042 . . . 4
21eqcomi 2470 . . 3
32preq2i 4113 . 2
4 opid.1 . . 3
54, 4dfop 4216 . 2
6 dfsn2 4042 . 2
73, 5, 63eqtr4i 2496 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  e.wcel 1818   cvv 3109  {csn 4029  {cpr 4031  <.cop 4035
This theorem is referenced by:  dmsnsnsn  5491  funopg  5625
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036
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