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Theorem ord0 4393
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 4114 . 2  |-  Tr  (/)
2 ral0 3526 . 2  |-  A. x  e.  (/)  Tr  x
3 dford3 4369 . 2  |-  ( Ord  (/) 
<->  ( Tr  (/)  /\  A. x  e.  (/)  Tr  x
) )
41, 2, 3mpbir2an 942 1  |-  Ord  (/)
Colors of variables: wff set class
Syntax hints:   A.wral 2455   (/)c0 3424   Tr wtr 4103   Ord word 4364
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-v 2741  df-dif 3133  df-in 3137  df-ss 3144  df-nul 3425  df-pw 3579  df-uni 3812  df-tr 4104  df-iord 4368
This theorem is referenced by:  0elon  4394  ordtriexmidlem  4520  2ordpr  4525  smo0  6301
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