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Theorem ord0 4444
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 4124 . 2  |-  Tr  (/)
2 we0 4388 . 2  |-  _E  We  (/)
3 df-ord 4395 . 2  |-  ( Ord  (/) 
<->  ( Tr  (/)  /\  _E  We  (/) ) )
41, 2, 3mpbir2an 886 1  |-  Ord  (/)
Colors of variables: wff set class
Syntax hints:   (/)c0 3455   Tr wtr 4113    _E cep 4303    We wwe 4351   Ord word 4391
This theorem is referenced by:  0elon  4445  ord0eln0  4446  ordzsl  4636  smo0  6375  oicl  7244  alephgeom  7709
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-in 3159  df-ss 3166  df-nul 3456  df-pw 3627  df-uni 3828  df-tr 4114  df-po 4314  df-so 4315  df-fr 4352  df-we 4354  df-ord 4395
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