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Theorem tpcomb 4230
 Description: Swap 2nd and 3rd members of an unordered triple. (Contributed by NM, 22-May-2015.)
Assertion
Ref Expression
tpcomb {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}

Proof of Theorem tpcomb
StepHypRef Expression
1 tpcoma 4229 . 2 {𝐵, 𝐶, 𝐴} = {𝐶, 𝐵, 𝐴}
2 tprot 4228 . 2 {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴}
3 tprot 4228 . 2 {𝐴, 𝐶, 𝐵} = {𝐶, 𝐵, 𝐴}
41, 2, 33eqtr4i 2642 1 {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475  {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-3or 1032  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-sn 4126  df-pr 4128  df-tp 4130 This theorem is referenced by:  f13dfv  6430  cusgra3v  25993  frgra3v  26529  signswch  29964  signstfvcl  29976  dvh4dimN  35754  frgr3v  41445
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