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Theorem tpcoma 4082
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 4064 . . 3  |-  { A ,  B }  =  { B ,  A }
21uneq1i 3617 . 2  |-  ( { A ,  B }  u.  { C } )  =  ( { B ,  A }  u.  { C } )
3 df-tp 3993 . 2  |-  { A ,  B ,  C }  =  ( { A ,  B }  u.  { C } )
4 df-tp 3993 . 2  |-  { B ,  A ,  C }  =  ( { B ,  A }  u.  { C } )
52, 3, 43eqtr4i 2493 1  |-  { A ,  B ,  C }  =  { B ,  A ,  C }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370    u. cun 3437   {csn 3988   {cpr 3990   {ctp 3992
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3080  df-un 3444  df-pr 3991  df-tp 3993
This theorem is referenced by:  tpcomb  4083  tppreqb  4125  nb3grapr2  23541  nb3gra2nb  23542  frgra3v  30765  3vfriswmgra  30768  1to3vfriswmgra  30770
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