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Theorem tpid1 3666
 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
tpid1.1
Assertion
Ref Expression
tpid1

Proof of Theorem tpid1
StepHypRef Expression
1 eqid 2154 . . 3
213mix1i 1154 . 2
3 tpid1.1 . . 3
43eltp 3603 . 2
52, 4mpbir 145 1
 Colors of variables: wff set class Syntax hints:   w3o 962   wceq 1332   wcel 2125  cvv 2709  ctp 3558 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-3or 964  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711  df-un 3102  df-sn 3562  df-pr 3563  df-tp 3564 This theorem is referenced by:  tpnz  3680
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