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Theorem ord0 4218
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 3947 . 2  |-  Tr  (/)
2 ral0 3383 . 2  |-  A. x  e.  (/)  Tr  x
3 dford3 4194 . 2  |-  ( Ord  (/) 
<->  ( Tr  (/)  /\  A. x  e.  (/)  Tr  x
) )
41, 2, 3mpbir2an 888 1  |-  Ord  (/)
Colors of variables: wff set class
Syntax hints:   A.wral 2359   (/)c0 3286   Tr wtr 3936   Ord word 4189
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-v 2621  df-dif 3001  df-in 3005  df-ss 3012  df-nul 3287  df-pw 3431  df-uni 3654  df-tr 3937  df-iord 4193
This theorem is referenced by:  0elon  4219  ordtriexmidlem  4336  2ordpr  4340  smo0  6063
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