Theorem tpcomb 3818

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 3817	. 2 ⊢ {B, C, A} = {C, B, A}
2		tprot 3816	. 2 ⊢ {A, B, C} = {B, C, A}
3		tprot 3816	. 2 ⊢ {A, C, B} = {C, B, A}
4	1, 2, 3	3eqtr4i 2383	1 ⊢ {A, B, C} = {A, C, B}

Syntax hints:   = wceq 1642  {ctp 3740

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-v 2862  df-nin 3212  df-compl 3213  df-un 3215  df-sn 3742  df-pr 3743  df-tp 3744

This theorem is referenced by: (None)