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Theorem df3o2 40239
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 8095 . 2 3o = suc 2o
2 df2o3 8108 . . . 4 2o = {∅, 1o}
32uneq1i 4139 . . 3 (2o ∪ {2o}) = ({∅, 1o} ∪ {2o})
4 df-suc 6195 . . 3 suc 2o = (2o ∪ {2o})
5 df-tp 4569 . . 3 {∅, 1o, 2o} = ({∅, 1o} ∪ {2o})
63, 4, 53eqtr4i 2859 . 2 suc 2o = {∅, 1o, 2o}
71, 6eqtri 2849 1 3o = {∅, 1o, 2o}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1530  cun 3938  c0 4295  {csn 4564  {cpr 4566  {ctp 4568  suc csuc 6191  1oc1o 8086  2oc2o 8087  3oc3o 8088
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-v 3502  df-dif 3943  df-un 3945  df-nul 4296  df-pr 4567  df-tp 4569  df-suc 6195  df-1o 8093  df-2o 8094  df-3o 8095
This theorem is referenced by:  clsk1indlem4  40259  clsk1indlem1  40260
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