Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  preq12i Structured version   Unicode version

Theorem preq12i 3890
 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 3887 . 2
41, 2, 3mp2an 655 1
 Colors of variables: wff set class Syntax hints:   wceq 1653  cpr 3817 This theorem is referenced by:  grpbasex  13574  grpplusgx  13575  indistpsx  17076  lgsdir2lem5  21113  wlkntrllem2  21562  tgrpset  31604 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-un 3327  df-sn 3822  df-pr 3823
 Copyright terms: Public domain W3C validator