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Theorem ontrci 4689
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 4688 . 2  |-  Ord  A
3 ordtr 4597 . 2  |-  ( Ord 
A  ->  Tr  A
)
42, 3ax-mp 8 1  |-  Tr  A
Colors of variables: wff set class
Syntax hints:    e. wcel 1726   Tr wtr 4304   Ord word 4582   Oncon0 4583
This theorem is referenced by:  onunisuci  4697  hfuni  26127
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-v 2960  df-in 3329  df-ss 3336  df-uni 4018  df-tr 4305  df-po 4505  df-so 4506  df-fr 4543  df-we 4545  df-ord 4586  df-on 4587
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