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Theorem tpidm13 3866
Description: Unordered triple  { A ,  B ,  A } is just an overlong way to write  { A ,  B }. (Contributed by David A. Wheeler, 10-May-2015.)
Assertion
Ref Expression
tpidm13  |-  { A ,  B ,  A }  =  { A ,  B }

Proof of Theorem tpidm13
StepHypRef Expression
1 tprot 3859 . 2  |-  { A ,  A ,  B }  =  { A ,  B ,  A }
2 tpidm12 3865 . 2  |-  { A ,  A ,  B }  =  { A ,  B }
31, 2eqtr3i 2426 1  |-  { A ,  B ,  A }  =  { A ,  B }
Colors of variables: wff set class
Syntax hints:    = wceq 1649   {cpr 3775   {ctp 3776
This theorem is referenced by:  hashtpg  11646
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 2385
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-v 2918  df-un 3285  df-sn 3780  df-pr 3781  df-tp 3782
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