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Theorem opeqpr 4749
 Description: Equivalence for an ordered pair equal to an unordered pair. (Contributed by NM, 3-Jun-2008.) (Avoid depending on this detail.)
Hypotheses
Ref Expression
opeqpr.1
opeqpr.2
opeqpr.3
opeqpr.4
Assertion
Ref Expression
opeqpr

Proof of Theorem opeqpr
StepHypRef Expression
1 eqcom 2466 . 2
2 opeqpr.1 . . . 4
3 opeqpr.2 . . . 4
42, 3dfop 4216 . . 3
54eqeq2i 2475 . 2
6 opeqpr.3 . . 3
7 opeqpr.4 . . 3
8 snex 4693 . . 3
9 prex 4694 . . 3
106, 7, 8, 9preq12b 4206 . 2
111, 5, 103bitri 271 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  \/wo 368  /\wa 369  =wceq 1395  e.wcel 1818   cvv 3109  {csn 4029  {cpr 4031  <.cop 4035 This theorem is referenced by:  relop  5158 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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 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-ne 2654  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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