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Theorem ordin 4422
 Description: The intersection of two ordinal classes is ordinal. Proposition 7.9 of [TakeutiZaring] p. 37. (Contributed by NM, 9-May-1994.)
Assertion
Ref Expression
ordin

Proof of Theorem ordin
StepHypRef Expression
1 ordtr 4406 . . 3
2 ordtr 4406 . . 3
3 trin 4123 . . 3
41, 2, 3syl2an 463 . 2
5 inss2 3390 . . 3
6 trssord 4409 . . 3
75, 6mp3an2 1265 . 2
84, 7sylancom 648 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   cin 3151   wss 3152   wtr 4113   word 4391 This theorem is referenced by:  onin  4423  ordtri3or  4424  ordelinel  4491  smores  6369  smores2  6371  ordtypelem5  7237  ordtypelem7  7239 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-v 2790  df-in 3159  df-ss 3166  df-uni 3828  df-tr 4114  df-po 4314  df-so 4315  df-fr 4352  df-we 4354  df-ord 4395
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