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Theorem tpidm 3910
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 3907 . 2  |-  { A ,  A ,  A }  =  { A ,  A }
2 dfsn2 3830 . 2  |-  { A }  =  { A ,  A }
31, 2eqtr4i 2461 1  |-  { A ,  A ,  A }  =  { A }
Colors of variables: wff set class
Syntax hints:    = wceq 1653   {csn 3816   {cpr 3817   {ctp 3818
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-un 3327  df-pr 3823  df-tp 3824
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