MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  tpcomb Structured version   Unicode version

Theorem tpcomb 4094
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 4093 . 2  |-  { B ,  C ,  A }  =  { C ,  B ,  A }
2 tprot 4092 . 2  |-  { A ,  B ,  C }  =  { B ,  C ,  A }
3 tprot 4092 . 2  |-  { A ,  C ,  B }  =  { C ,  B ,  A }
41, 2, 33eqtr4i 2461 1  |-  { A ,  B ,  C }  =  { A ,  C ,  B }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437   {ctp 4000
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3or 983  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-v 3083  df-un 3441  df-sn 3997  df-pr 3999  df-tp 4001
This theorem is referenced by:  f13dfv  6185  cusgra3v  25178  frgra3v  25716  signswch  29446  signstfvcl  29458  dvh4dimN  34934
  Copyright terms: Public domain W3C validator