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Theorem df3o2 41093
 Description: Ordinal 3 is the unordered triple 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 8115 . 2 3o = suc 2o
2 df2o3 8128 . . . 4 2o = {∅, 1o}
32uneq1i 4065 . . 3 (2o ∪ {2o}) = ({∅, 1o} ∪ {2o})
4 df-suc 6176 . . 3 suc 2o = (2o ∪ {2o})
5 df-tp 4528 . . 3 {∅, 1o, 2o} = ({∅, 1o} ∪ {2o})
63, 4, 53eqtr4i 2792 . 2 suc 2o = {∅, 1o, 2o}
71, 6eqtri 2782 1 3o = {∅, 1o, 2o}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1539   ∪ cun 3857  ∅c0 4226  {csn 4523  {cpr 4525  {ctp 4527  suc csuc 6172  1oc1o 8106  2oc2o 8107  3oc3o 8108 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-9 2122  ax-ext 2730 This theorem depends on definitions:  df-bi 210  df-an 401  df-or 846  df-tru 1542  df-ex 1783  df-sb 2071  df-clab 2737  df-cleq 2751  df-clel 2831  df-v 3412  df-dif 3862  df-un 3864  df-nul 4227  df-pr 4526  df-tp 4528  df-suc 6176  df-1o 8113  df-2o 8114  df-3o 8115 This theorem is referenced by:  clsk1indlem4  41113  clsk1indlem1  41114
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