MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  tpidm13 Structured version   Unicode version

Theorem tpidm13 4077
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 4070 . 2  |-  { A ,  A ,  B }  =  { A ,  B ,  A }
2 tpidm12 4076 . 2  |-  { A ,  A ,  B }  =  { A ,  B }
31, 2eqtr3i 2482 1  |-  { A ,  B ,  A }  =  { A ,  B }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370   {cpr 3979   {ctp 3981
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 1952  ax-ext 2430
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 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-v 3072  df-un 3433  df-sn 3978  df-pr 3980  df-tp 3982
This theorem is referenced by:  hashtpg  12290
  Copyright terms: Public domain W3C validator