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Theorem 0lt2o 11885
Description: Ordinal zero is less than ordinal two. (Contributed by Jim Kingdon, 31-Jul-2022.)
Assertion
Ref Expression
0lt2o ∅ ∈ 2𝑜

Proof of Theorem 0lt2o
StepHypRef Expression
1 0ex 3966 . . 3 ∅ ∈ V
21prid1 3548 . 2 ∅ ∈ {∅, 1𝑜}
3 df2o3 6195 . 2 2𝑜 = {∅, 1𝑜}
42, 3eleqtrri 2163 1 ∅ ∈ 2𝑜
Colors of variables: wff set class
Syntax hints:  wcel 1438  c0 3286  {cpr 3447  1𝑜c1o 6174  2𝑜c2o 6175
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-nul 3965
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-dif 3001  df-un 3003  df-nul 3287  df-sn 3452  df-pr 3453  df-suc 4198  df-1o 6181  df-2o 6182
This theorem is referenced by:  0nninf  11893  nninfalllemn  11898  nninfsellemcl  11903
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