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Theorem ord0 6110
Description: The empty set is an ordinal class. (Contributed by NM, 11-May-1994.)
Assertion
Ref Expression
ord0 Ord ∅

Proof of Theorem ord0
StepHypRef Expression
1 tr0 5068 . 2 Tr ∅
2 we0 5430 . 2 E We ∅
3 df-ord 6061 . 2 (Ord ∅ ↔ (Tr ∅ ∧ E We ∅))
41, 2, 3mpbir2an 707 1 Ord ∅
Colors of variables: wff setvar class
Syntax hints:  c0 4206  Tr wtr 5057   E cep 5344   We wwe 5393  Ord word 6057
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1775  ax-4 1789  ax-5 1886  ax-6 1945  ax-7 1990  ax-8 2081  ax-9 2089  ax-10 2110  ax-11 2124  ax-12 2139  ax-ext 2767
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-tru 1523  df-ex 1760  df-nf 1764  df-sb 2041  df-clab 2774  df-cleq 2786  df-clel 2861  df-nfc 2933  df-ne 2983  df-ral 3108  df-rex 3109  df-rab 3112  df-v 3434  df-dif 3857  df-in 3861  df-ss 3869  df-nul 4207  df-pw 4449  df-uni 4740  df-tr 5058  df-po 5354  df-so 5355  df-fr 5394  df-we 5396  df-ord 6061
This theorem is referenced by:  0elon  6111  ord0eln0  6112  ordzsl  7407  smo0  7838  oicl  8829  alephgeom  9343
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