Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  tpeq3 Structured version   Unicode version

Theorem tpeq3 3896
 Description: Equality theorem for unordered triples. (Contributed by NM, 13-Sep-2011.)
Assertion
Ref Expression
tpeq3

Proof of Theorem tpeq3
StepHypRef Expression
1 sneq 3827 . . 3
21uneq2d 3503 . 2
3 df-tp 3824 . 2
4 df-tp 3824 . 2
52, 3, 43eqtr4g 2495 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   cun 3320  csn 3816  cpr 3817  ctp 3818 This theorem is referenced by:  tpeq3d  3899  tppreq3  3911  fztpval  11109  hashtpg  11693  dvh4dimN  32307 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-tp 3824
 Copyright terms: Public domain W3C validator