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Theorem dfop 4216
 Description: Value of an ordered pair when the arguments are sets, with the conclusion corresponding to Kuratowski's original definition. (Contributed by NM, 25-Jun-1998.) (Avoid depending on this detail.)
Hypotheses
Ref Expression
dfop.1
dfop.2
Assertion
Ref Expression
dfop

Proof of Theorem dfop
StepHypRef Expression
1 dfop.1 . 2
2 dfop.2 . 2
3 dfopg 4215 . 2
41, 2, 3mp2an 672 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:  opid  4236  elop  4718  opi1  4719  opi2  4720  op1stb  4722  opeqsn  4748  opeqpr  4749  uniop  4755  xpsspw  5121  xpsspwOLD  5122  relop  5158  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-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-op 4036
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