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Theorem 0lt2o 6304
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 4023 . . 3 ∅ ∈ V
21prid1 3597 . 2 ∅ ∈ {∅, 1o}
3 df2o3 6293 . 2 2o = {∅, 1o}
42, 3eleqtrri 2191 1 ∅ ∈ 2o
Colors of variables: wff set class
Syntax hints:  wcel 1463  c0 3331  {cpr 3496  1oc1o 6272  2oc2o 6273
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-nul 4022
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-dif 3041  df-un 3043  df-nul 3332  df-sn 3501  df-pr 3502  df-suc 4261  df-1o 6279  df-2o 6280
This theorem is referenced by:  fodjuf  6983  mkvprop  6998  unct  11849  pwle2  13004  subctctexmid  13007  0nninf  13008  nninfalllemn  13013  nninfsellemcl  13018  nninffeq  13027  isomninnlem  13036
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