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Theorem tpid1 4143
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 2457 . . 3
213mix1i 1168 . 2
3 tpid1.1 . . 3
43eltp 4074 . 2
52, 4mpbir 209 1
Colors of variables: wff setvar class
Syntax hints:  \/w3o 972  =wceq 1395  e.wcel 1818   cvv 3109  {ctp 4033
This theorem is referenced by:  tpnz  4151  2pthlem2  24598  usgra2adedgwlkonALT  24616  sgnsf  27719  sgncl  28477  kur14lem7  28656  kur14lem9  28658  brtpid1  29098  rabren3dioph  30749  fourierdlem102  31991  fourierdlem114  32003  etransclem48  32065
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-3or 974  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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