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Theorem tpcoma 3843
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 3825 . . 3  |-  { A ,  B }  =  { B ,  A }
21uneq1i 3440 . 2  |-  ( { A ,  B }  u.  { C } )  =  ( { B ,  A }  u.  { C } )
3 df-tp 3765 . 2  |-  { A ,  B ,  C }  =  ( { A ,  B }  u.  { C } )
4 df-tp 3765 . 2  |-  { B ,  A ,  C }  =  ( { B ,  A }  u.  { C } )
52, 3, 43eqtr4i 2417 1  |-  { A ,  B ,  C }  =  { B ,  A ,  C }
Colors of variables: wff set class
Syntax hints:    = wceq 1649    u. cun 3261   {csn 3757   {cpr 3758   {ctp 3759
This theorem is referenced by:  tpcomb  3844  tppreqb  3882  nb3grapr2  21329  nb3gra2nb  21330  frgra3v  27755  3vfriswmgra  27758  1to3vfriswmgra  27760
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 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-v 2901  df-un 3268  df-pr 3764  df-tp 3765
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