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Theorem preq12d 3617
 Description: Equality deduction for unordered pairs. (Contributed by NM, 19-Oct-2012.)
Hypotheses
Ref Expression
preq1d.1
preq12d.2
Assertion
Ref Expression
preq12d

Proof of Theorem preq12d
StepHypRef Expression
1 preq1d.1 . 2
2 preq12d.2 . 2
3 preq12 3611 . 2
41, 2, 3syl2anc 409 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1332  cpr 3534 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-un 3081  df-sn 3539  df-pr 3540 This theorem is referenced by:  opeq1  3714  opeq2  3715  xrminrecl  11094  xrminadd  11096  xmetxp  12735  xmetxpbl  12736  txmetcnp  12746
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