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Theorem onn0 6420
Description: The class of all ordinal numbers is not empty. (Contributed by NM, 17-Sep-1995.)
Assertion
Ref Expression
onn0 On ≠ ∅

Proof of Theorem onn0
StepHypRef Expression
1 0elon 6409 . 2 ∅ ∈ On
21ne0ii 4330 1 On ≠ ∅
Colors of variables: wff setvar class
Syntax hints:  wne 2932  c0 4315  Oncon0 6355
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-nul 5297
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-ne 2933  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-pw 4597  df-sn 4622  df-pr 4624  df-op 4628  df-uni 4901  df-br 5140  df-tr 5257  df-po 5579  df-so 5580  df-fr 5622  df-we 5624  df-ord 6358  df-on 6359
This theorem is referenced by:  limon  7818
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