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Theorem tpidm23 4757
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 4749 . 2 {𝐴, 𝐵, 𝐵} = {𝐵, 𝐵, 𝐴}
2 tpidm12 4755 . 2 {𝐵, 𝐵, 𝐴} = {𝐵, 𝐴}
3 prcom 4732 . 2 {𝐵, 𝐴} = {𝐴, 𝐵}
41, 2, 33eqtri 2769 1 {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  {cpr 4628  {ctp 4630
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3or 1088  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-un 3956  df-sn 4627  df-pr 4629  df-tp 4631
This theorem is referenced by:  tppreq3  4759  fntpb  7229  hashtpg  14524  hash3tpde  14532
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