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Theorem tpidm 4686
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 4683 . 2 {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴}
2 dfsn2 4570 . 2 {𝐴} = {𝐴, 𝐴}
31, 2eqtr4i 2844 1 {𝐴, 𝐴, 𝐴} = {𝐴}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1528  {csn 4557  {cpr 4559  {ctp 4561
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-v 3494  df-un 3938  df-pr 4560  df-tp 4562
This theorem is referenced by: (None)
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