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Theorem 0lt2o 6268
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 3995 . . 3  |-  (/)  e.  _V
21prid1 3576 . 2  |-  (/)  e.  { (/)
,  1o }
3 df2o3 6257 . 2  |-  2o  =  { (/) ,  1o }
42, 3eleqtrri 2175 1  |-  (/)  e.  2o
Colors of variables: wff set class
Syntax hints:    e. wcel 1448   (/)c0 3310   {cpr 3475   1oc1o 6236   2oc2o 6237
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 584  ax-in2 585  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082  ax-nul 3994
This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-v 2643  df-dif 3023  df-un 3025  df-nul 3311  df-sn 3480  df-pr 3481  df-suc 4231  df-1o 6243  df-2o 6244
This theorem is referenced by:  fodjuf  6929  mkvprop  6943  pwle2  12779  0nninf  12781  nninfalllemn  12786  nninfsellemcl  12791  nninffeq  12800  isomninnlem  12809
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