Description: The image of a singleton outside the domain is empty. (Contributed by NM, 22-May-1998) (Proof shortened by OpenAI, 3-Jul-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | ndmima | |- ( -. A e. dom B -> ( B " { A } ) = (/) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imadisj | |- ( ( B " { A } ) = (/) <-> ( dom B i^i { A } ) = (/) ) |
|
2 | disjsn | |- ( ( dom B i^i { A } ) = (/) <-> -. A e. dom B ) |
|
3 | 1 2 | sylbbr | |- ( -. A e. dom B -> ( B " { A } ) = (/) ) |