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Theorem tpidm13 4692
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 4685 . 2 {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵, 𝐴}
2 tpidm12 4691 . 2 {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵}
31, 2eqtr3i 2768 1 {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  {cpr 4563  {ctp 4565
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3or 1087  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-un 3892  df-sn 4562  df-pr 4564  df-tp 4566
This theorem is referenced by:  fntpb  7085  hashtpg  14199
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