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Theorem tpcoma 3892
Description: Swap 1st and 2nd members of an undordered triple. (Contributed by NM, 22-May-2015.)
Assertion
Ref Expression
tpcoma  |-  { A ,  B ,  C }  =  { B ,  A ,  C }

Proof of Theorem tpcoma
StepHypRef Expression
1 prcom 3874 . . 3  |-  { A ,  B }  =  { B ,  A }
21uneq1i 3489 . 2  |-  ( { A ,  B }  u.  { C } )  =  ( { B ,  A }  u.  { C } )
3 df-tp 3814 . 2  |-  { A ,  B ,  C }  =  ( { A ,  B }  u.  { C } )
4 df-tp 3814 . 2  |-  { B ,  A ,  C }  =  ( { B ,  A }  u.  { C } )
52, 3, 43eqtr4i 2465 1  |-  { A ,  B ,  C }  =  { B ,  A ,  C }
Colors of variables: wff set class
Syntax hints:    = wceq 1652    u. cun 3310   {csn 3806   {cpr 3807   {ctp 3808
This theorem is referenced by:  tpcomb  3893  tppreqb  3931  nb3grapr2  21455  nb3gra2nb  21456  frgra3v  28329  3vfriswmgra  28332  1to3vfriswmgra  28334
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-pr 3813  df-tp 3814
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