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Theorem tpcoma 4067
Description: Swap 1st and 2nd members of an unordered 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 4049 . . 3  |-  { A ,  B }  =  { B ,  A }
21uneq1i 3592 . 2  |-  ( { A ,  B }  u.  { C } )  =  ( { B ,  A }  u.  { C } )
3 df-tp 3976 . 2  |-  { A ,  B ,  C }  =  ( { A ,  B }  u.  { C } )
4 df-tp 3976 . 2  |-  { B ,  A ,  C }  =  ( { B ,  A }  u.  { C } )
52, 3, 43eqtr4i 2441 1  |-  { A ,  B ,  C }  =  { B ,  A ,  C }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1405    u. cun 3411   {csn 3971   {cpr 3973   {ctp 3975
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-v 3060  df-un 3418  df-pr 3974  df-tp 3976
This theorem is referenced by:  tpcomb  4068  tppreqb  4112  nb3grapr2  24752  nb3gra2nb  24753  frgra3v  25300  3vfriswmgra  25303  1to3vfriswmgra  25305
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