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Theorem tpeq1 3808
Description: Equality theorem for unordered triples. (Contributed by NM, 13-Sep-2011.)
Assertion
Ref Expression
tpeq1

Proof of Theorem tpeq1
StepHypRef Expression
1 preq1 3799 . . 3
21uneq1d 3417 . 2
3 df-tp 3743 . 2
4 df-tp 3743 . 2
52, 3, 43eqtr4g 2410 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wceq 1642   cun 3207  csn 3737  cpr 3738  ctp 3739
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-sn 3741  df-pr 3742  df-tp 3743
This theorem is referenced by:  tpeq1d  3811
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