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Theorem tpidm12 4234
 Description: Unordered triple {𝐴, 𝐴, 𝐵} is just an overlong way to write {𝐴, 𝐵}. (Contributed by David A. Wheeler, 10-May-2015.)
Assertion
Ref Expression
tpidm12 {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵}

Proof of Theorem tpidm12
StepHypRef Expression
1 dfsn2 4138 . . 3 {𝐴} = {𝐴, 𝐴}
21uneq1i 3725 . 2 ({𝐴} ∪ {𝐵}) = ({𝐴, 𝐴} ∪ {𝐵})
3 df-pr 4128 . 2 {𝐴, 𝐵} = ({𝐴} ∪ {𝐵})
4 df-tp 4130 . 2 {𝐴, 𝐴, 𝐵} = ({𝐴, 𝐴} ∪ {𝐵})
52, 3, 43eqtr4ri 2643 1 {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ∪ cun 3538  {csn 4125  {cpr 4127  {ctp 4129 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-pr 4128  df-tp 4130 This theorem is referenced by:  tpidm13  4235  tpidm23  4236  tpidm  4237  fntpb  6378  hashtpg  13121
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