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Theorem tpcoma 4276
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 4258 . . 3 {𝐴, 𝐵} = {𝐵, 𝐴}
21uneq1i 3755 . 2 ({𝐴, 𝐵} ∪ {𝐶}) = ({𝐵, 𝐴} ∪ {𝐶})
3 df-tp 4173 . 2 {𝐴, 𝐵, 𝐶} = ({𝐴, 𝐵} ∪ {𝐶})
4 df-tp 4173 . 2 {𝐵, 𝐴, 𝐶} = ({𝐵, 𝐴} ∪ {𝐶})
52, 3, 43eqtr4i 2652 1 {𝐴, 𝐵, 𝐶} = {𝐵, 𝐴, 𝐶}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1481  cun 3565  {csn 4168  {cpr 4170  {ctp 4172
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-v 3197  df-un 3572  df-pr 4171  df-tp 4173
This theorem is referenced by:  tpcomb  4277  tppreqb  4327  nb3grpr2  26266  nb3gr2nb  26267  frgr3v  27119  3vfriswmgr  27122  1to3vfriswmgr  27124
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