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Theorem df3o2 37843
Description: Ordinal 3 is the triplet containing ordinals 0, 1 and 2. (Contributed by RP, 8-Jul-2021.)
Assertion
Ref Expression
df3o2 3𝑜 = {∅, 1𝑜, 2𝑜}

Proof of Theorem df3o2
StepHypRef Expression
1 df-3o 7522 . 2 3𝑜 = suc 2𝑜
2 df2o3 7533 . . . 4 2𝑜 = {∅, 1𝑜}
32uneq1i 3747 . . 3 (2𝑜 ∪ {2𝑜}) = ({∅, 1𝑜} ∪ {2𝑜})
4 df-suc 5698 . . 3 suc 2𝑜 = (2𝑜 ∪ {2𝑜})
5 df-tp 4160 . . 3 {∅, 1𝑜, 2𝑜} = ({∅, 1𝑜} ∪ {2𝑜})
63, 4, 53eqtr4i 2653 . 2 suc 2𝑜 = {∅, 1𝑜, 2𝑜}
71, 6eqtri 2643 1 3𝑜 = {∅, 1𝑜, 2𝑜}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  cun 3558  c0 3897  {csn 4155  {cpr 4157  {ctp 4159  suc csuc 5694  1𝑜c1o 7513  2𝑜c2o 7514  3𝑜c3o 7515
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 3192  df-dif 3563  df-un 3565  df-nul 3898  df-pr 4158  df-tp 4160  df-suc 5698  df-1o 7520  df-2o 7521  df-3o 7522
This theorem is referenced by:  clsk1indlem4  37863  clsk1indlem1  37864
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