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Theorem tpid3 3484
 Description: One of the three elements of an unordered triple. (Contributed by NM, 7-Apr-1994.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Hypothesis
Ref Expression
tpid3.1
Assertion
Ref Expression
tpid3

Proof of Theorem tpid3
StepHypRef Expression
1 eqid 2040 . . 3
213mix3i 1078 . 2
3 tpid3.1 . . 3
43eltp 3418 . 2
52, 4mpbir 134 1
 Colors of variables: wff set class Syntax hints:   w3o 884   wceq 1243   wcel 1393  cvv 2557  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-3or 886  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: (None)
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