Metamath Proof Explorer

Theorem rnffi

Description: The range of a function with finite domain is finite. (Contributed by Glauco Siliprandi, 11-Dec-2019)

Ref Expression
Assertion rnffi 
|- ( ( F : A --> B /\ A e. Fin ) -> ran F e. Fin )

Proof

Step Hyp Ref Expression
1 ffi 
 |-  ( ( F : A --> B /\ A e. Fin ) -> F e. Fin )
2 rnfi 
 |-  ( F e. Fin -> ran F e. Fin )
3 1 2 syl 
 |-  ( ( F : A --> B /\ A e. Fin ) -> ran F e. Fin )