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Theorem 0lt2o 6345
Description: Ordinal zero is less than ordinal two. (Contributed by Jim Kingdon, 31-Jul-2022.)
Assertion
Ref Expression
0lt2o  |-  (/)  e.  2o

Proof of Theorem 0lt2o
StepHypRef Expression
1 0ex 4062 . . 3  |-  (/)  e.  _V
21prid1 3636 . 2  |-  (/)  e.  { (/)
,  1o }
3 df2o3 6334 . 2  |-  2o  =  { (/) ,  1o }
42, 3eleqtrri 2216 1  |-  (/)  e.  2o
Colors of variables: wff set class
Syntax hints:    e. wcel 1481   (/)c0 3367   {cpr 3532   1oc1o 6313   2oc2o 6314
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 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-nul 4061
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-dif 3077  df-un 3079  df-nul 3368  df-sn 3537  df-pr 3538  df-suc 4300  df-1o 6320  df-2o 6321
This theorem is referenced by:  fodjuf  7024  mkvprop  7039  unct  11989  012of  13361  pwle2  13364  subctctexmid  13367  0nninf  13370  nninfalllemn  13375  nninfsellemcl  13380  nninffeq  13389
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