Theorem tpidm23 3677

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 3669	. 2 |- { A , B , B } = { B , B , A }
2		tpidm12 3675	. 2 |- { B , B , A } = { B , A }
3		prcom 3652	. 2 |- { B , A } = { A , B }
4	1, 2, 3	3eqtri 2190	1 |- { A , B , B } = { A , B }

Syntax hints:   = wceq 1343   {cpr 3577   {ctp 3578

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-3or 969  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-v 2728  df-un 3120  df-sn 3582  df-pr 3583  df-tp 3584

This theorem is referenced by:  tppreq3  3679