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Theorem df2o3 6014
 Description: Expanded value of the ordinal number 2. (Contributed by Mario Carneiro, 14-Aug-2015.)
Assertion
Ref Expression
df2o3 2𝑜 = {∅, 1𝑜}

Proof of Theorem df2o3
StepHypRef Expression
1 df-2o 6002 . 2 2𝑜 = suc 1𝑜
2 df-suc 4108 . 2 suc 1𝑜 = (1𝑜 ∪ {1𝑜})
3 df1o2 6013 . . . 4 1𝑜 = {∅}
43uneq1i 3093 . . 3 (1𝑜 ∪ {1𝑜}) = ({∅} ∪ {1𝑜})
5 df-pr 3382 . . 3 {∅, 1𝑜} = ({∅} ∪ {1𝑜})
64, 5eqtr4i 2063 . 2 (1𝑜 ∪ {1𝑜}) = {∅, 1𝑜}
71, 2, 63eqtri 2064 1 2𝑜 = {∅, 1𝑜}
 Colors of variables: wff set class Syntax hints:   = wceq 1243   ∪ cun 2915  ∅c0 3224  {csn 3375  {cpr 3376  suc csuc 4102  1𝑜c1o 5994  2𝑜c2o 5995 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-dif 2920  df-un 2922  df-nul 3225  df-pr 3382  df-suc 4108  df-1o 6001  df-2o 6002 This theorem is referenced by:  df2o2  6015  2oconcl  6022
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