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Theorem tpidm13 4765
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 4758 . 2 {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵, 𝐴}
2 tpidm12 4764 . 2 {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵}
31, 2eqtr3i 2758 1 {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  {cpr 4634  {ctp 4636
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3or 1085  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3475  df-un 3954  df-sn 4633  df-pr 4635  df-tp 4637
This theorem is referenced by:  fntpb  7227  hashtpg  14486
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