Metamath Proof Explorer

Theorem fex

Description: If the domain of a mapping is a set, the function is a set. (Contributed by NM, 3-Oct-1999)

Ref Expression
Assertion fex 
|- ( ( F : A --> B /\ A e. C ) -> F e. _V )

Proof

Step Hyp Ref Expression
1 ffn 
 |-  ( F : A --> B -> F Fn A )
2 fnex 
 |-  ( ( F Fn A /\ A e. C ) -> F e. _V )
3 1 2 sylan 
 |-  ( ( F : A --> B /\ A e. C ) -> F e. _V )