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Theorem smodm 5847
Description: The domain of a strictly monotone function is an ordinal. (Contributed by Andrew Salmon, 16-Nov-2011.)
Assertion
Ref Expression
smodm (Smo A → Ord dom A)

Proof of Theorem smodm
Dummy variables x y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-smo 5842 . 2 (Smo A ↔ (A:dom A⟶On Ord dom A x dom Ay dom A(x y → (Ax) (Ay))))
21simp2bi 919 1 (Smo A → Ord dom A)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  wral 2300  Ord word 4065  Oncon0 4066  dom cdm 4288  wf 4841  cfv 4845  Smo wsmo 5841
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100
This theorem depends on definitions:  df-bi 110  df-3an 886  df-smo 5842
This theorem is referenced by:  smores2  5850  smodm2  5851  smoel  5856
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