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Theorem tpcomb 4056
Description: Swap 2nd and 3rd members of an unordered triple. (Contributed by NM, 22-May-2015.)
Assertion
Ref Expression
tpcomb  |-  { A ,  B ,  C }  =  { A ,  C ,  B }

Proof of Theorem tpcomb
StepHypRef Expression
1 tpcoma 4055 . 2  |-  { B ,  C ,  A }  =  { C ,  B ,  A }
2 tprot 4054 . 2  |-  { A ,  B ,  C }  =  { B ,  C ,  A }
3 tprot 4054 . 2  |-  { A ,  C ,  B }  =  { C ,  B ,  A }
41, 2, 33eqtr4i 2488 1  |-  { A ,  B ,  C }  =  { A ,  C ,  B }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370   {ctp 3965
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1709  ax-7 1729  ax-10 1776  ax-11 1781  ax-12 1793  ax-13 1944  ax-ext 2429
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 966  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1702  df-clab 2436  df-cleq 2442  df-clel 2445  df-nfc 2598  df-v 3056  df-un 3417  df-sn 3962  df-pr 3964  df-tp 3966
This theorem is referenced by:  cusgra3v  23493  signswch  27082  signstfvcl  27094  f13dfv  30271  frgra3v  30718  dvh4dimN  35374
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