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Theorem ord0 6211
 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 5147 . 2 Tr ∅
2 we0 5514 . 2 E We ∅
3 df-ord 6162 . 2 (Ord ∅ ↔ (Tr ∅ ∧ E We ∅))
41, 2, 3mpbir2an 710 1 Ord ∅
 Colors of variables: wff setvar class Syntax hints:  ∅c0 4243  Tr wtr 5136   E cep 5429   We wwe 5477  Ord word 6158 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ne 2988  df-ral 3111  df-rex 3112  df-rab 3115  df-v 3443  df-dif 3884  df-in 3888  df-ss 3898  df-nul 4244  df-pw 4499  df-uni 4801  df-tr 5137  df-po 5438  df-so 5439  df-fr 5478  df-we 5480  df-ord 6162 This theorem is referenced by:  0elon  6212  ord0eln0  6213  ordzsl  7542  smo0  7980  oicl  8979  alephgeom  9495
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