Metamath Proof Explorer

Theorem elpmi2

Description: The domain of a partial function. (Contributed by Glauco Siliprandi, 26-Jun-2021)

Ref Expression
Assertion elpmi2 
|- ( F e. ( A ^pm B ) -> dom F C_ B )

Proof

Step Hyp Ref Expression
1 elpmi 
 |-  ( F e. ( A ^pm B ) -> ( F : dom F --> A /\ dom F C_ B ) )
2 1 simprd 
 |-  ( F e. ( A ^pm B ) -> dom F C_ B )