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Theorem tpidm23 4101
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 4093 . 2  |-  { A ,  B ,  B }  =  { B ,  B ,  A }
2 tpidm12 4099 . 2  |-  { B ,  B ,  A }  =  { B ,  A }
3 prcom 4076 . 2  |-  { B ,  A }  =  { A ,  B }
41, 2, 33eqtri 2456 1  |-  { A ,  B ,  B }  =  { A ,  B }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1438   {cpr 3999   {ctp 4001
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3or 984  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-v 3084  df-un 3442  df-sn 3998  df-pr 4000  df-tp 4002
This theorem is referenced by:  tppreq3  4103  hashtpg  12639
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