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Theorem df2o3 6045
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 6033 . 2 2𝑜 = suc 1𝑜
2 df-suc 4136 . 2 suc 1𝑜 = (1𝑜 ∪ {1𝑜})
3 df1o2 6044 . . . 4 1𝑜 = {∅}
43uneq1i 3121 . . 3 (1𝑜 ∪ {1𝑜}) = ({∅} ∪ {1𝑜})
5 df-pr 3410 . . 3 {∅, 1𝑜} = ({∅} ∪ {1𝑜})
64, 5eqtr4i 2079 . 2 (1𝑜 ∪ {1𝑜}) = {∅, 1𝑜}
71, 2, 63eqtri 2080 1 2𝑜 = {∅, 1𝑜}
Colors of variables: wff set class
Syntax hints:   = wceq 1259  cun 2943  c0 3252  {csn 3403  {cpr 3404  suc csuc 4130  1𝑜c1o 6025  2𝑜c2o 6026
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-dif 2948  df-un 2950  df-nul 3253  df-pr 3410  df-suc 4136  df-1o 6032  df-2o 6033
This theorem is referenced by:  df2o2  6046  2oconcl  6053
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