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Theorem df3o2 38741
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 7682 . 2 3𝑜 = suc 2𝑜
2 df2o3 7693 . . . 4 2𝑜 = {∅, 1𝑜}
32uneq1i 3871 . . 3 (2𝑜 ∪ {2𝑜}) = ({∅, 1𝑜} ∪ {2𝑜})
4 df-suc 5842 . . 3 suc 2𝑜 = (2𝑜 ∪ {2𝑜})
5 df-tp 4290 . . 3 {∅, 1𝑜, 2𝑜} = ({∅, 1𝑜} ∪ {2𝑜})
63, 4, 53eqtr4i 2756 . 2 suc 2𝑜 = {∅, 1𝑜, 2𝑜}
71, 6eqtri 2746 1 3𝑜 = {∅, 1𝑜, 2𝑜}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1596  cun 3678  c0 4023  {csn 4285  {cpr 4287  {ctp 4289  suc csuc 5838  1𝑜c1o 7673  2𝑜c2o 7674  3𝑜c3o 7675
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-10 2132  ax-11 2147  ax-12 2160  ax-13 2355  ax-ext 2704
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-nfc 2855  df-v 3306  df-dif 3683  df-un 3685  df-nul 4024  df-pr 4288  df-tp 4290  df-suc 5842  df-1o 7680  df-2o 7681  df-3o 7682
This theorem is referenced by:  clsk1indlem4  38761  clsk1indlem1  38762
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