Metamath Proof Explorer

Theorem smodm

Description: The domain of a strictly monotone function is an ordinal. (Contributed by Andrew Salmon, 16-Nov-2011)

Ref Expression
Assertion smodm 
|- ( Smo A -> Ord dom A )

Proof

Step Hyp Ref Expression
1 df-smo 
 |-  ( Smo A <-> ( A : dom A --> On /\ Ord dom A /\ A. x e. dom A A. y e. dom A ( x e. y -> ( A ` x ) e. ( A ` y ) ) ) )
2 1 simp2bi 
 |-  ( Smo A -> Ord dom A )