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Theorem tpidm23 4081
Description: Unordered triple  { A ,  B ,  B } is just an overlong way to write  { A ,  B }. (Contributed by David A. Wheeler, 10-May-2015.)
Assertion
Ref Expression
tpidm23  |-  { A ,  B ,  B }  =  { A ,  B }

Proof of Theorem tpidm23
StepHypRef Expression
1 tprot 4073 . 2  |-  { A ,  B ,  B }  =  { B ,  B ,  A }
2 tpidm12 4079 . 2  |-  { B ,  B ,  A }  =  { B ,  A }
3 prcom 4056 . 2  |-  { B ,  A }  =  { A ,  B }
41, 2, 33eqtri 2485 1  |-  { A ,  B ,  B }  =  { A ,  B }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370   {cpr 3982   {ctp 3984
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1954  ax-ext 2431
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 966  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2602  df-v 3074  df-un 3436  df-sn 3981  df-pr 3983  df-tp 3985
This theorem is referenced by:  tppreq3  4083  hashtpg  12299
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