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Theorem tpcomb 4263
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 4262 . 2 {𝐵, 𝐶, 𝐴} = {𝐶, 𝐵, 𝐴}
2 tprot 4261 . 2 {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴}
3 tprot 4261 . 2 {𝐴, 𝐶, 𝐵} = {𝐶, 𝐵, 𝐴}
41, 2, 33eqtr4i 2653 1 {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  {ctp 4159
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3or 1037  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3192  df-un 3565  df-sn 4156  df-pr 4158  df-tp 4160
This theorem is referenced by:  f13dfv  6495  frgr3v  27037  signswch  30460  signstfvcl  30472  dvh4dimN  36255
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