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Theorem 0lt1o 7536
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 2621 . 2 ∅ = ∅
2 el1o 7531 . 2 (∅ ∈ 1𝑜 ↔ ∅ = ∅)
31, 2mpbir 221 1 ∅ ∈ 1𝑜
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  wcel 1987  c0 3896  1𝑜c1o 7505
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-nul 4754
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3191  df-dif 3562  df-un 3564  df-nul 3897  df-sn 4154  df-suc 5693  df-1o 7512
This theorem is referenced by:  dif20el  7537  oe1m  7577  oen0  7618  oeoa  7629  oeoe  7631  isfin4-3  9089  fin1a2lem4  9177  1lt2pi  9679  indpi  9681  sadcp1  15112  vr1cl2  19495  fvcoe1  19509  vr1cl  19519  subrgvr1cl  19564  coe1mul2lem1  19569  coe1tm  19575  ply1coe  19598  evl1var  19632  evls1var  19634  xkofvcn  21410  pw2f1ocnv  37119  wepwsolem  37127
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