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Theorem preq12i 4114
Description: Equality inference for unordered pairs. (Contributed by NM, 19-Oct-2012.)
Hypotheses
Ref Expression
preq1i.1
preq12i.2
Assertion
Ref Expression
preq12i

Proof of Theorem preq12i
StepHypRef Expression
1 preq1i.1 . 2
2 preq12i.2 . 2
3 preq12 4111 . 2
41, 2, 3mp2an 672 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  {cpr 4031
This theorem is referenced by:  grpbasex  14740  grpplusgx  14741  indistpsx  19511  lgsdir2lem5  23602  wlkntrllem2  24562  clwwlkgt0  24771  zlmodzxzadd  32947  zlmodzxzequa  33097  zlmodzxzequap  33100  tgrpset  36471
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-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-un 3480  df-sn 4030  df-pr 4032
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