Theorem tpcomb 4286

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

Step	Hyp	Ref	Expression
1		tpcoma 4285	. 2 |- { B , C , A } = { C , B , A }
2		tprot 4284	. 2 |- { A , B , C } = { B , C , A }
3		tprot 4284	. 2 |- { A , C , B } = { C , B , A }
4	1, 2, 3	3eqtr4i 2654	1 |- { A , B , C } = { A , C , B }

Syntax hints:   = wceq 1483   {ctp 4181

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3or 1038  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-un 3579  df-sn 4178  df-pr 4180  df-tp 4182

This theorem is referenced by:  f13dfv  6530  frgr3v  27139  signswch  30638  signstfvcl  30650  dvh4dimN  36736