Theorem tpcoma 3521

Description: Swap 1st and 2nd members of an undordered triple. (Contributed by NM, 22-May-2015.)

Assertion

Ref	Expression
tpcoma	|- { A , B , C } = { B , A , C }

Proof of Theorem tpcoma

Step	Hyp	Ref	Expression
1		prcom 3503	. . 3 |- { A , B } = { B , A }
2	1	uneq1i 3139	. 2 |- ( { A , B } u. { C } ) = ( { B , A } u. { C } )
3		df-tp 3439	. 2 |- { A , B , C } = ( { A , B } u. { C } )
4		df-tp 3439	. 2 |- { B , A , C } = ( { B , A } u. { C } )
5	2, 3, 4	3eqtr4i 2115	1 |- { A , B , C } = { B , A , C }

Syntax hints:   = wceq 1287   u. cun 2986   {csn 3431   {cpr 3432   {ctp 3433

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067

This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617  df-un 2992  df-pr 3438  df-tp 3439

This theorem is referenced by:  tpcomb  3522