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Theorem ord0 4148
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 3888 . 2  |-  Tr  (/)
2 ral0 3344 . 2  |-  A. x  e.  (/)  Tr  x
3 dford3 4124 . 2  |-  ( Ord  (/) 
<->  ( Tr  (/)  /\  A. x  e.  (/)  Tr  x
) )
41, 2, 3mpbir2an 884 1  |-  Ord  (/)
Colors of variables: wff set class
Syntax hints:   A.wral 2349   (/)c0 3252   Tr wtr 3877   Ord word 4119
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 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-v 2604  df-dif 2976  df-in 2980  df-ss 2987  df-nul 3253  df-pw 3386  df-uni 3604  df-tr 3878  df-iord 4123
This theorem is referenced by:  0elon  4149  ordtriexmidlem  4265  2ordpr  4269  smo0  5941
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