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Theorem tpid2 4144
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
tpid2.1
Assertion
Ref Expression
tpid2

Proof of Theorem tpid2
StepHypRef Expression
1 eqid 2457 . . 3
213mix2i 1169 . 2
3 tpid2.1 . . 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:  2pthlem1  24597  2pthlem2  24598  el2wlkonotlem  24862  sgnsf  27719  sgncl  28477  signsw0glem  28510  signsw0g  28513  signswmnd  28514  signswrid  28515  kur14lem7  28656  brtpid2  29099  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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