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Theorem trssord 4900
Description: A transitive subclass of an ordinal class is ordinal. (Contributed by NM, 29-May-1994.)
Assertion
Ref Expression
trssord

Proof of Theorem trssord
StepHypRef Expression
1 ordwe 4896 . . . . 5
2 wess 4871 . . . . . 6
32imp 429 . . . . 5
41, 3sylan2 474 . . . 4
54anim2i 569 . . 3
653impb 1192 . 2
7 df-ord 4886 . 2
86, 7sylibr 212 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  C_wss 3475  Trwtr 4545   cep 4794  Wewwe 4842  Ordword 4882
This theorem is referenced by:  ordin  4913  ssorduni  6621  suceloni  6648  ordom  6709  ordtypelem2  7965  hartogs  7990  card2on  8001  tskwe  8352  ondomon  8959  dford3lem2  30969  dford3  30970
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-in 3482  df-ss 3489  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886
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