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Theorem tpcomb 3869
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 3868 . 2  |-  { B ,  C ,  A }  =  { C ,  B ,  A }
2 tprot 3867 . 2  |-  { A ,  B ,  C }  =  { B ,  C ,  A }
3 tprot 3867 . 2  |-  { A ,  C ,  B }  =  { C ,  B ,  A }
41, 2, 33eqtr4i 2442 1  |-  { A ,  B ,  C }  =  { A ,  C ,  B }
Colors of variables: wff set class
Syntax hints:    = wceq 1649   {ctp 3784
This theorem is referenced by:  cusgra3v  21434  f13dfv  27970  frgra3v  28114  dvh4dimN  31942
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-v 2926  df-un 3293  df-sn 3788  df-pr 3789  df-tp 3790
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