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Theorem tpcoma 4094
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 4076 . . 3  |-  { A ,  B }  =  { B ,  A }
21uneq1i 3617 . 2  |-  ( { A ,  B }  u.  { C } )  =  ( { B ,  A }  u.  { C } )
3 df-tp 4002 . 2  |-  { A ,  B ,  C }  =  ( { A ,  B }  u.  { C } )
4 df-tp 4002 . 2  |-  { B ,  A ,  C }  =  ( { B ,  A }  u.  { C } )
52, 3, 43eqtr4i 2462 1  |-  { A ,  B ,  C }  =  { B ,  A ,  C }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1438    u. cun 3435   {csn 3997   {cpr 3999   {ctp 4001
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-v 3084  df-un 3442  df-pr 4000  df-tp 4002
This theorem is referenced by:  tpcomb  4095  tppreqb  4139  nb3grapr2  25174  nb3gra2nb  25175  frgra3v  25722  3vfriswmgra  25725  1to3vfriswmgra  25727
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