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Theorem ord0 4283
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 4007 . 2  |-  Tr  (/)
2 ral0 3434 . 2  |-  A. x  e.  (/)  Tr  x
3 dford3 4259 . 2  |-  ( Ord  (/) 
<->  ( Tr  (/)  /\  A. x  e.  (/)  Tr  x
) )
41, 2, 3mpbir2an 911 1  |-  Ord  (/)
Colors of variables: wff set class
Syntax hints:   A.wral 2393   (/)c0 3333   Tr wtr 3996   Ord word 4254
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ral 2398  df-v 2662  df-dif 3043  df-in 3047  df-ss 3054  df-nul 3334  df-pw 3482  df-uni 3707  df-tr 3997  df-iord 4258
This theorem is referenced by:  0elon  4284  ordtriexmidlem  4405  2ordpr  4409  smo0  6163
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