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Theorem tpidm13 4122
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 4115 . 2  |-  { A ,  A ,  B }  =  { A ,  B ,  A }
2 tpidm12 4121 . 2  |-  { A ,  A ,  B }  =  { A ,  B }
31, 2eqtr3i 2491 1  |-  { A ,  B ,  A }  =  { A ,  B }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1374   {cpr 4022   {ctp 4024
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 969  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-v 3108  df-un 3474  df-sn 4021  df-pr 4023  df-tp 4025
This theorem is referenced by:  hashtpg  12476
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