Metamath Proof Explorer


Theorem smofvon

Description: If B is a strictly monotone ordinal function, and A is in the domain of B , then the value of the function at A is an ordinal. (Contributed by Andrew Salmon, 20-Nov-2011)

Ref Expression
Assertion smofvon Smo B A dom B B A On

Proof

Step Hyp Ref Expression
1 df-smo Smo B B : dom B On Ord dom B x dom B y dom B x y B x B y
2 1 simp1bi Smo B B : dom B On
3 2 ffvelrnda Smo B A dom B B A On