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Theorem tpidm13 4647
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 4640 . 2 {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵, 𝐴}
2 tpidm12 4646 . 2 {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵}
31, 2eqtr3i 2763 1 {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  {cpr 4518  {ctp 4520
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-3or 1089  df-tru 1545  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-v 3400  df-un 3848  df-sn 4517  df-pr 4519  df-tp 4521
This theorem is referenced by:  fntpb  6982  hashtpg  13937
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