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Theorem tpeq2 4119
 Description: Equality theorem for unordered triples. (Contributed by NM, 13-Sep-2011.)
Assertion
Ref Expression
tpeq2

Proof of Theorem tpeq2
StepHypRef Expression
1 preq2 4110 . . 3
21uneq1d 3656 . 2
3 df-tp 4034 . 2
4 df-tp 4034 . 2
52, 3, 43eqtr4g 2523 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395  u.cun 3473  {csn 4029  {cpr 4031  {ctp 4033 This theorem is referenced by:  tpeq2d  4122  fztpval  11770  hashtpg  12523  lmod1  33093  dvh4dimN  37174 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  df-tp 4034
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