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Theorem prcom 3446
 Description: Commutative law for unordered pairs. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
prcom

Proof of Theorem prcom
StepHypRef Expression
1 uncom 3087 . 2
2 df-pr 3382 . 2
3 df-pr 3382 . 2
41, 2, 33eqtr4i 2070 1
 Colors of variables: wff set class Syntax hints:   wceq 1243   cun 2915  csn 3375  cpr 3376 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-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-pr 3382 This theorem is referenced by:  preq2  3448  tpcoma  3464  tpidm23  3471  prid2g  3475  prid2  3477  prprc2  3479  difprsn2  3504  preqr2g  3538  preqr2  3540  preq12b  3541  fvpr2  5366  fvpr2g  5368
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