Metamath Proof Explorer

Theorem frnd

Description: Deduction form of frn . The range of a mapping. (Contributed by Glauco Siliprandi, 26-Jun-2021)

Ref Expression
Hypothesis frnd.1 
|- ( ph -> F : A --> B )
Assertion frnd 
|- ( ph -> ran F C_ B )

Proof

Step Hyp Ref Expression
1 frnd.1 
 |-  ( ph -> F : A --> B )
2 frn 
 |-  ( F : A --> B -> ran F C_ B )
3 1 2 syl 
 |-  ( ph -> ran F C_ B )