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Theorem ontrci 4245
Description: An ordinal number is a transitive class. (Contributed by NM, 11-Jun-1994.)
Hypothesis
Ref Expression
on.1  |-  A  e.  On
Assertion
Ref Expression
ontrci  |-  Tr  A

Proof of Theorem ontrci
StepHypRef Expression
1 on.1 . . 3  |-  A  e.  On
21onordi 4244 . 2  |-  Ord  A
3 ordtr 4196 . 2  |-  ( Ord 
A  ->  Tr  A
)
42, 3ax-mp 7 1  |-  Tr  A
Colors of variables: wff set class
Syntax hints:    e. wcel 1438   Tr wtr 3928   Ord word 4180   Oncon0 4181
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-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-rex 2365  df-v 2621  df-in 3003  df-ss 3010  df-uni 3649  df-tr 3929  df-iord 4184  df-on 4186
This theorem is referenced by:  onunisuci  4250  nnsf  11541
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