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Theorem tpidm 4263
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 4260 . 2 {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴}
2 dfsn2 4161 . 2 {𝐴} = {𝐴, 𝐴}
31, 2eqtr4i 2646 1 {𝐴, 𝐴, 𝐴} = {𝐴}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  {csn 4148  {cpr 4150  {ctp 4152
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3188  df-un 3560  df-pr 4151  df-tp 4153
This theorem is referenced by: (None)
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