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Theorem 0lt1o 6348
 Description: Ordinal zero is less than ordinal one. (Contributed by NM, 5-Jan-2005.)
Assertion
Ref Expression
0lt1o

Proof of Theorem 0lt1o
StepHypRef Expression
1 eqid 2140 . 2
2 el1o 6345 . 2
31, 2mpbir 145 1
 Colors of variables: wff set class Syntax hints:   wceq 1332   wcel 1481  c0 3369  c1o 6317 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 4063 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 2692  df-dif 3079  df-un 3081  df-nul 3370  df-sn 3539  df-suc 4303  df-1o 6324 This theorem is referenced by:  nnaordex  6434  1domsn  6724  snexxph  6854  difinfsnlem  7000  difinfsn  7001  0ct  7008  ctmlemr  7009  ctssdclemn0  7011  exmidfodomrlemr  7085  exmidfodomrlemrALT  7086  1lt2pi  7199  archnqq  7276  prarloclemarch2  7278  pwle2  13409
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