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Theorem tpcomb 3724
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 3723 . 2  |-  { B ,  C ,  A }  =  { C ,  B ,  A }
2 tprot 3722 . 2  |-  { A ,  B ,  C }  =  { B ,  C ,  A }
3 tprot 3722 . 2  |-  { A ,  C ,  B }  =  { C ,  B ,  A }
41, 2, 33eqtr4i 2313 1  |-  { A ,  B ,  C }  =  { A ,  C ,  B }
Colors of variables: wff set class
Syntax hints:    = wceq 1623   {ctp 3642
This theorem is referenced by:  frgra3v  28180  dvh4dimN  31637
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-sn 3646  df-pr 3647  df-tp 3648
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