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Theorem tpcomb 4113
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 4112 . 2  |-  { B ,  C ,  A }  =  { C ,  B ,  A }
2 tprot 4111 . 2  |-  { A ,  B ,  C }  =  { B ,  C ,  A }
3 tprot 4111 . 2  |-  { A ,  C ,  B }  =  { C ,  B ,  A }
41, 2, 33eqtr4i 2493 1  |-  { A ,  B ,  C }  =  { A ,  C ,  B }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1398   {ctp 4020
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3or 972  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3108  df-un 3466  df-sn 4017  df-pr 4019  df-tp 4021
This theorem is referenced by:  f13dfv  6155  cusgra3v  24669  frgra3v  25207  signswch  28785  signstfvcl  28797  dvh4dimN  37590
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