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Theorem ord0 4880
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 4505 . 2  |-  Tr  (/)
2 we0 4824 . 2  |-  _E  We  (/)
3 df-ord 4831 . 2  |-  ( Ord  (/) 
<->  ( Tr  (/)  /\  _E  We  (/) ) )
41, 2, 3mpbir2an 911 1  |-  Ord  (/)
Colors of variables: wff setvar class
Syntax hints:   (/)c0 3746   Tr wtr 4494    _E cep 4739    We wwe 4787   Ord word 4827
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3440  df-in 3444  df-ss 3451  df-nul 3747  df-pw 3971  df-uni 4201  df-tr 4495  df-po 4750  df-so 4751  df-fr 4788  df-we 4790  df-ord 4831
This theorem is referenced by:  0elon  4881  ord0eln0  4882  ordzsl  6567  smo0  6930  oicl  7855  alephgeom  8364
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