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Theorem tpidm 3542
Description: Unordered triple  { A ,  A ,  A } is just an overlong way to write  { A }. (Contributed by David A. Wheeler, 10-May-2015.)
Assertion
Ref Expression
tpidm  |-  { A ,  A ,  A }  =  { A }

Proof of Theorem tpidm
StepHypRef Expression
1 tpidm12 3539 . 2  |-  { A ,  A ,  A }  =  { A ,  A }
2 dfsn2 3458 . 2  |-  { A }  =  { A ,  A }
31, 2eqtr4i 2111 1  |-  { A ,  A ,  A }  =  { A }
Colors of variables: wff set class
Syntax hints:    = wceq 1289   {csn 3444   {cpr 3445   {ctp 3446
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3003  df-pr 3451  df-tp 3452
This theorem is referenced by: (None)
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