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Theorem tpidm23 4078
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 4070 . 2  |-  { A ,  B ,  B }  =  { B ,  B ,  A }
2 tpidm12 4076 . 2  |-  { B ,  B ,  A }  =  { B ,  A }
3 prcom 4053 . 2  |-  { B ,  A }  =  { A ,  B }
41, 2, 33eqtri 2479 1  |-  { A ,  B ,  B }  =  { A ,  B }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1446   {cpr 3972   {ctp 3974
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3or 987  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-v 3049  df-un 3411  df-sn 3971  df-pr 3973  df-tp 3975
This theorem is referenced by:  tppreq3  4080  hashtpg  12648
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