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Theorem 0lt1o 6740
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 2435 . 2  |-  (/)  =  (/)
2 el1o 6735 . 2  |-  ( (/)  e.  1o  <->  (/)  =  (/) )
31, 2mpbir 201 1  |-  (/)  e.  1o
Colors of variables: wff set class
Syntax hints:    = wceq 1652    e. wcel 1725   (/)c0 3620   1oc1o 6709
This theorem is referenced by:  dif20el  6741  oe1m  6780  oen0  6821  oeoa  6832  oeoe  6834  cantnf0  7622  isfin4-3  8187  fin1a2lem4  8275  1lt2pi  8774  indpi  8776  sadcp1  12959  vr1cl2  16583  fvcoe1  16597  vr1cl  16603  subrgvr1cl  16647  coe1mul2lem1  16652  coe1tm  16657  ply1coe  16676  xkofvcn  17708  evl1var  19944  pw2f1ocnv  27099  wepwsolem  27107
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-nul 4330
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-dif 3315  df-un 3317  df-nul 3621  df-sn 3812  df-suc 4579  df-1o 6716
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