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Theorem 0lt1o 6438
Description: Ordinal zero is less than ordinal one. (Contributed by NM, 5-Jan-2005.)
Assertion
Ref Expression
0lt1o  |-  (/)  e.  1o

Proof of Theorem 0lt1o
StepHypRef Expression
1 eqid 2177 . 2  |-  (/)  =  (/)
2 el1o 6435 . 2  |-  ( (/)  e.  1o  <->  (/)  =  (/) )
31, 2mpbir 146 1  |-  (/)  e.  1o
Colors of variables: wff set class
Syntax hints:    = wceq 1353    e. wcel 2148   (/)c0 3422   1oc1o 6407
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 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-nul 4128
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-dif 3131  df-un 3133  df-nul 3423  df-sn 3598  df-suc 4370  df-1o 6414
This theorem is referenced by:  nnaordex  6526  1domsn  6816  snexxph  6946  difinfsnlem  7095  difinfsn  7096  0ct  7103  ctmlemr  7104  ctssdclemn0  7106  exmidfodomrlemr  7198  exmidfodomrlemrALT  7199  1lt2pi  7336  archnqq  7413  prarloclemarch2  7415  pwle2  14608
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