Metamath Proof Explorer


Theorem frn

Description: The range of a mapping. (Contributed by NM, 3-Aug-1994)

Ref Expression
Assertion frn
|- ( F : A --> B -> ran F C_ B )

Proof

Step Hyp Ref Expression
1 df-f
 |-  ( F : A --> B <-> ( F Fn A /\ ran F C_ B ) )
2 1 simprbi
 |-  ( F : A --> B -> ran F C_ B )