Theorem tpidm23 3776

Description: Unordered triple { A , B , B } is just an overlong way to write { A , B }. (Contributed by David A. Wheeler, 10-May-2015.)

Assertion

Ref	Expression
tpidm23	|- { A , B , B } = { A , B }

Proof of Theorem tpidm23

Step	Hyp	Ref	Expression
1		tprot 3768	. 2 |- { A , B , B } = { B , B , A }
2		tpidm12 3774	. 2 |- { B , B , A } = { B , A }
3		prcom 3751	. 2 |- { B , A } = { A , B }
4	1, 2, 3	3eqtri 2256	1 |- { A , B , B } = { A , B }

Syntax hints:   = wceq 1398   {cpr 3674   {ctp 3675

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 2213

This theorem depends on definitions:  df-bi 117  df-3or 1006  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-v 2805  df-un 3205  df-sn 3679  df-pr 3680  df-tp 3681

This theorem is referenced by:  tppreq3  3778  hashtpglem  11173