ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  0lt2o Unicode version

Theorem 0lt2o 6466
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 4145 . . 3  |-  (/)  e.  _V
21prid1 3713 . 2  |-  (/)  e.  { (/)
,  1o }
3 df2o3 6455 . 2  |-  2o  =  { (/) ,  1o }
42, 3eleqtrri 2265 1  |-  (/)  e.  2o
Colors of variables: wff set class
Syntax hints:    e. wcel 2160   (/)c0 3437   {cpr 3608   1oc1o 6434   2oc2o 6435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-nul 4144
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-dif 3146  df-un 3148  df-nul 3438  df-sn 3613  df-pr 3614  df-suc 4389  df-1o 6441  df-2o 6442
This theorem is referenced by:  nnnninf  7154  nnnninfeq  7156  fodjuf  7173  mkvprop  7186  nninfwlporlemd  7200  nninfwlporlem  7201  nninfwlpoimlemg  7203  nninfwlpoimlemginf  7204  2oneel  7285  2omotaplemst  7287  unct  12493  xpsfeq  12821  xpsfval  12824  xpsval  12828  bj-charfun  15020  bj-charfundc  15021  012of  15207  pwle2  15210  subctctexmid  15212  0nninf  15215  nninfsellemcl  15222  nninffeq  15231
  Copyright terms: Public domain W3C validator