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Theorem opcom 4015
 Description: An ordered pair commutes iff its members are equal. (Contributed by NM, 28-May-2009.)
Hypotheses
Ref Expression
opcom.1
opcom.2
Assertion
Ref Expression
opcom

Proof of Theorem opcom
StepHypRef Expression
1 opcom.1 . . 3
2 opcom.2 . . 3
31, 2opth 4002 . 2
4 eqcom 2058 . . 3
54anbi2i 438 . 2
6 anidm 382 . 2
73, 5, 63bitri 199 1
 Colors of variables: wff set class Syntax hints:   wa 101   wb 102   wceq 1259   wcel 1409  cvv 2574  cop 3406 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-pow 3955  ax-pr 3972 This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-pw 3389  df-sn 3409  df-pr 3410  df-op 3412 This theorem is referenced by: (None)
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