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Theorem smodm2 7045
Description: The domain of a strictly monotone ordinal function is an ordinal. (Contributed by Mario Carneiro, 12-Mar-2013.)
Assertion
Ref Expression
smodm2

Proof of Theorem smodm2
StepHypRef Expression
1 smodm 7041 . 2
2 fndm 5685 . . . 4
3 ordeq 4890 . . . 4
42, 3syl 16 . . 3
54biimpa 484 . 2
61, 5sylan2 474 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  Ordword 4882  domcdm 5004  Fnwfn 5588  Smowsmo 7035
This theorem is referenced by:  smo11  7054  smoord  7055  smoword  7056  smogt  7057  smorndom  7058  coftr  8674
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-nfc 2607  df-ral 2812  df-rex 2813  df-in 3482  df-ss 3489  df-uni 4250  df-tr 4546  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886  df-fn 5596  df-smo 7036
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