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Theorem tpidm 3872
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 3869 . 2  |-  { A ,  A ,  A }  =  { A ,  A }
2 dfsn2 3792 . 2  |-  { A }  =  { A ,  A }
31, 2eqtr4i 2431 1  |-  { A ,  A ,  A }  =  { A }
Colors of variables: wff set class
Syntax hints:    = wceq 1649   {csn 3778   {cpr 3779   {ctp 3780
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-v 2922  df-un 3289  df-pr 3785  df-tp 3786
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