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Theorem tpeq123d 3462
 Description: Equality theorem for unordered triples. (Contributed by NM, 22-Jun-2014.)
Hypotheses
Ref Expression
tpeq1d.1
tpeq123d.2
tpeq123d.3
Assertion
Ref Expression
tpeq123d

Proof of Theorem tpeq123d
StepHypRef Expression
1 tpeq1d.1 . . 3
21tpeq1d 3459 . 2
3 tpeq123d.2 . . 3
43tpeq2d 3460 . 2
5 tpeq123d.3 . . 3
65tpeq3d 3461 . 2
72, 4, 63eqtrd 2076 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243  ctp 3377 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-tp 3383 This theorem is referenced by:  fz0tp  8981  fzo0to3tp  9075
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