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Theorem tpidm 3472
 Description: Unordered triple {𝐴, 𝐴, 𝐴} is just an overlong way to write {𝐴}. (Contributed by David A. Wheeler, 10-May-2015.)
Assertion
Ref Expression
tpidm {𝐴, 𝐴, 𝐴} = {𝐴}

Proof of Theorem tpidm
StepHypRef Expression
1 tpidm12 3469 . 2 {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴}
2 dfsn2 3389 . 2 {𝐴} = {𝐴, 𝐴}
31, 2eqtr4i 2063 1 {𝐴, 𝐴, 𝐴} = {𝐴}
 Colors of variables: wff set class Syntax hints:   = wceq 1243  {csn 3375  {cpr 3376  {ctp 3377 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-pr 3382  df-tp 3383 This theorem is referenced by: (None)
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