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Theorem ord0 4460
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 4140 . 2  |-  Tr  (/)
2 we0 4404 . 2  |-  _E  We  (/)
3 df-ord 4411 . 2  |-  ( Ord  (/) 
<->  ( Tr  (/)  /\  _E  We  (/) ) )
41, 2, 3mpbir2an 886 1  |-  Ord  (/)
Colors of variables: wff set class
Syntax hints:   (/)c0 3468   Tr wtr 4129    _E cep 4319    We wwe 4367   Ord word 4407
This theorem is referenced by:  0elon  4461  ord0eln0  4462  ordzsl  4652  smo0  6391  oicl  7260  alephgeom  7725
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-in 3172  df-ss 3179  df-nul 3469  df-pw 3640  df-uni 3844  df-tr 4130  df-po 4330  df-so 4331  df-fr 4368  df-we 4370  df-ord 4411
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