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Theorem tpcoma 4229
 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 4211 . . 3 {𝐴, 𝐵} = {𝐵, 𝐴}
21uneq1i 3725 . 2 ({𝐴, 𝐵} ∪ {𝐶}) = ({𝐵, 𝐴} ∪ {𝐶})
3 df-tp 4130 . 2 {𝐴, 𝐵, 𝐶} = ({𝐴, 𝐵} ∪ {𝐶})
4 df-tp 4130 . 2 {𝐵, 𝐴, 𝐶} = ({𝐵, 𝐴} ∪ {𝐶})
52, 3, 43eqtr4i 2642 1 {𝐴, 𝐵, 𝐶} = {𝐵, 𝐴, 𝐶}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ∪ cun 3538  {csn 4125  {cpr 4127  {ctp 4129 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-pr 4128  df-tp 4130 This theorem is referenced by:  tpcomb  4230  tppreqb  4277  nb3grapr2  25983  nb3gra2nb  25984  frgra3v  26529  3vfriswmgra  26532  1to3vfriswmgra  26534  nb3grpr2  40611  nb3gr2nb  40612  frgr3v  41445  3vfriswmgr  41448  1to3vfriswmgr  41450
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