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Theorem tpidm12 3821
 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 3747 . . 3 {A} = {A, A}
21uneq1i 3414 . 2 ({A} ∪ {B}) = ({A, A} ∪ {B})
3 df-pr 3742 . 2 {A, B} = ({A} ∪ {B})
4 df-tp 3743 . 2 {A, A, B} = ({A, A} ∪ {B})
52, 3, 43eqtr4ri 2384 1 {A, A, B} = {A, B}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∪ cun 3207  {csn 3737  {cpr 3738  {ctp 3739 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-pr 3742  df-tp 3743 This theorem is referenced by:  tpidm13  3822  tpidm23  3823  tpidm  3824
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