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Theorem ord0 4633
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 4313 . 2  |-  Tr  (/)
2 we0 4577 . 2  |-  _E  We  (/)
3 df-ord 4584 . 2  |-  ( Ord  (/) 
<->  ( Tr  (/)  /\  _E  We  (/) ) )
41, 2, 3mpbir2an 887 1  |-  Ord  (/)
Colors of variables: wff set class
Syntax hints:   (/)c0 3628   Tr wtr 4302    _E cep 4492    We wwe 4540   Ord word 4580
This theorem is referenced by:  0elon  4634  ord0eln0  4635  ordzsl  4825  smo0  6620  oicl  7498  alephgeom  7963
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-in 3327  df-ss 3334  df-nul 3629  df-pw 3801  df-uni 4016  df-tr 4303  df-po 4503  df-so 4504  df-fr 4541  df-we 4543  df-ord 4584
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