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Theorem tpidm 4668
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 4665 . 2 {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴}
2 dfsn2 4552 . 2 {𝐴} = {𝐴, 𝐴}
31, 2eqtr4i 2848 1 {𝐴, 𝐴, 𝐴} = {𝐴}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  {csn 4539  {cpr 4541  {ctp 4543
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-v 3471  df-un 3913  df-pr 4542  df-tp 4544
This theorem is referenced by: (None)
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