Theorem tpcomb 3788

Description: Swap 2nd and 3rd members of an undordered 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 3787	. 2 |- { B , C , A } = { C , B , A }
2		tprot 3786	. 2 |- { A , B , C } = { B , C , A }
3		tprot 3786	. 2 |- { A , C , B } = { C , B , A }
4	1, 2, 3	3eqtr4i 2265	1 |- { A , B , C } = { A , C , B }

Syntax hints:   = wceq 1398   {ctp 3693

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-3or 1006  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-v 2817  df-un 3217  df-sn 3697  df-pr 3698  df-tp 3699

This theorem is referenced by:  prsstp13  3850