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Theorem 0lt1o 6344
 Description: Ordinal zero is less than ordinal one. (Contributed by NM, 5-Jan-2005.)
Assertion
Ref Expression
0lt1o ∅ ∈ 1o

Proof of Theorem 0lt1o
StepHypRef Expression
1 eqid 2140 . 2 ∅ = ∅
2 el1o 6341 . 2 (∅ ∈ 1o ↔ ∅ = ∅)
31, 2mpbir 145 1 ∅ ∈ 1o
 Colors of variables: wff set class Syntax hints:   = wceq 1332   ∈ wcel 1481  ∅c0 3367  1oc1o 6313 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-suc 4300  df-1o 6320 This theorem is referenced by:  nnaordex  6430  1domsn  6720  snexxph  6845  difinfsnlem  6991  difinfsn  6992  0ct  6999  ctmlemr  7000  ctssdclemn0  7002  exmidfodomrlemr  7074  exmidfodomrlemrALT  7075  1lt2pi  7171  archnqq  7248  prarloclemarch2  7250  pwle2  13364
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