Metamath Proof Explorer

Theorem fnfvelrn

Description: A function's value belongs to its range. (Contributed by NM, 15-Oct-1996)

Ref Expression
Assertion fnfvelrn 
|- ( ( F Fn A /\ B e. A ) -> ( F ` B ) e. ran F )

Proof

Step Hyp Ref Expression
1 fvelrn 
 |-  ( ( Fun F /\ B e. dom F ) -> ( F ` B ) e. ran F )
2 1 funfni 
 |-  ( ( F Fn A /\ B e. A ) -> ( F ` B ) e. ran F )