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Theorem tpidm13 4722
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 4715 . 2 {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵, 𝐴}
2 tpidm12 4721 . 2 {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵}
31, 2eqtr3i 2767 1 {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  {cpr 4593  {ctp 4595
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 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3or 1089  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-v 3450  df-un 3920  df-sn 4592  df-pr 4594  df-tp 4596
This theorem is referenced by:  fntpb  7164  hashtpg  14391
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