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Theorem tpcomb 3925
Description: Swap 2nd and 3rd members of an undordered 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 3924 . 2  |-  { B ,  C ,  A }  =  { C ,  B ,  A }
2 tprot 3923 . 2  |-  { A ,  B ,  C }  =  { B ,  C ,  A }
3 tprot 3923 . 2  |-  { A ,  C ,  B }  =  { C ,  B ,  A }
41, 2, 33eqtr4i 2472 1  |-  { A ,  B ,  C }  =  { A ,  C ,  B }
Colors of variables: wff set class
Syntax hints:    = wceq 1653   {ctp 3840
This theorem is referenced by:  cusgra3v  21504  f13dfv  28123  frgra3v  28490  dvh4dimN  32343
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-v 2964  df-un 3311  df-sn 3844  df-pr 3845  df-tp 3846
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