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Theorem tpidm 3675
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 3672 . 2 {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴}
2 dfsn2 3587 . 2 {𝐴} = {𝐴, 𝐴}
31, 2eqtr4i 2188 1 {𝐴, 𝐴, 𝐴} = {𝐴}
Colors of variables: wff set class
Syntax hints:   = wceq 1342  {csn 3573  {cpr 3574  {ctp 3575
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146
This theorem depends on definitions:  df-bi 116  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-v 2726  df-un 3118  df-pr 3580  df-tp 3581
This theorem is referenced by: (None)
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