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Theorem tpidm23 3528
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
StepHypRef Expression
1 tprot 3520 . 2  |-  { A ,  B ,  B }  =  { B ,  B ,  A }
2 tpidm12 3526 . 2  |-  { B ,  B ,  A }  =  { B ,  A }
3 prcom 3503 . 2  |-  { B ,  A }  =  { A ,  B }
41, 2, 33eqtri 2109 1  |-  { A ,  B ,  B }  =  { A ,  B }
Colors of variables: wff set class
Syntax hints:    = wceq 1287   {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-3or 923  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-sn 3437  df-pr 3438  df-tp 3439
This theorem is referenced by:  tppreq3  3530
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