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Theorem tpidm12 3460
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 3381 . . 3 {A} = {A, A}
21uneq1i 3087 . 2 ({A} ∪ {B}) = ({A, A} ∪ {B})
3 df-pr 3374 . 2 {A, B} = ({A} ∪ {B})
4 df-tp 3375 . 2 {A, A, B} = ({A, A} ∪ {B})
52, 3, 43eqtr4ri 2068 1 {A, A, B} = {A, B}
Colors of variables: wff set class
Syntax hints:   = wceq 1242  cun 2909  {csn 3367  {cpr 3368  {ctp 3369
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-pr 3374  df-tp 3375
This theorem is referenced by:  tpidm13  3461  tpidm23  3462  tpidm  3463
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