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Theorem ord0 4935
Description: The empty set is an ordinal class. (Contributed by NM, 11-May-1994.)
Assertion
Ref Expression
ord0

Proof of Theorem ord0
StepHypRef Expression
1 tr0 4556 . 2
2 we0 4879 . 2
3 df-ord 4886 . 2
41, 2, 3mpbir2an 920 1
Colors of variables: wff setvar class
Syntax hints:   c0 3784  Trwtr 4545   cep 4794  Wewwe 4842  Ordword 4882
This theorem is referenced by:  0elon  4936  ord0eln0  4937  ordzsl  6680  smo0  7048  oicl  7975  alephgeom  8484
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-pw 4014  df-uni 4250  df-tr 4546  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886
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