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Theorem ord0 6424
Description: The empty set is an ordinal class. Remark 1.5 of [Schloeder] p. 1. (Contributed by NM, 11-May-1994.)
Assertion
Ref Expression
ord0 Ord ∅

Proof of Theorem ord0
StepHypRef Expression
1 tr0 5279 . 2 Tr ∅
2 we0 5673 . 2 E We ∅
3 df-ord 6374 . 2 (Ord ∅ ↔ (Tr ∅ ∧ E We ∅))
41, 2, 3mpbir2an 709 1 Ord ∅
Colors of variables: wff setvar class
Syntax hints:  c0 4322  Tr wtr 5266   E cep 5581   We wwe 5632  Ord word 6370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-ne 2930  df-ral 3051  df-rex 3060  df-rab 3419  df-v 3463  df-dif 3947  df-un 3949  df-ss 3961  df-nul 4323  df-if 4531  df-pw 4606  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4910  df-br 5150  df-tr 5267  df-po 5590  df-so 5591  df-fr 5633  df-we 5635  df-ord 6374
This theorem is referenced by:  0elon  6425  ord0eln0  6426  ordzsl  7850  smo0  8379  oicl  9554  alephgeom  10107
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