Description: The predicate "is a partial function." (Contributed by NM, 15-Nov-2007) (Revised by Mario Carneiro, 31-Dec-2013)
Ref | Expression | ||
---|---|---|---|
Hypotheses | elmap.1 | |- A e. _V |
|
elmap.2 | |- B e. _V |
||
Assertion | elpm2 | |- ( F e. ( A ^pm B ) <-> ( F : dom F --> A /\ dom F C_ B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elmap.1 | |- A e. _V |
|
2 | elmap.2 | |- B e. _V |
|
3 | elpm2g | |- ( ( A e. _V /\ B e. _V ) -> ( F e. ( A ^pm B ) <-> ( F : dom F --> A /\ dom F C_ B ) ) ) |
|
4 | 1 2 3 | mp2an | |- ( F e. ( A ^pm B ) <-> ( F : dom F --> A /\ dom F C_ B ) ) |