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Theorem tpidm23 4755
Description: Unordered triple {𝐴, 𝐵, 𝐵} is just an overlong way to write {𝐴, 𝐵}. (Contributed by David A. Wheeler, 10-May-2015.)
Assertion
Ref Expression
tpidm23 {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵}

Proof of Theorem tpidm23
StepHypRef Expression
1 tprot 4747 . 2 {𝐴, 𝐵, 𝐵} = {𝐵, 𝐵, 𝐴}
2 tpidm12 4753 . 2 {𝐵, 𝐵, 𝐴} = {𝐵, 𝐴}
3 prcom 4730 . 2 {𝐵, 𝐴} = {𝐴, 𝐵}
41, 2, 33eqtri 2764 1 {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1541  {cpr 4625  {ctp 4627
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3or 1088  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-un 3950  df-sn 4624  df-pr 4626  df-tp 4628
This theorem is referenced by:  tppreq3  4757  fntpb  7196  hashtpg  14430
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