Description: An open set is a neighborhood of any of its members. (Contributed by NM, 8-Mar-2007)
Ref | Expression | ||
---|---|---|---|
Assertion | opnneip | |- ( ( J e. Top /\ N e. J /\ P e. N ) -> N e. ( ( nei ` J ) ` { P } ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snssi | |- ( P e. N -> { P } C_ N ) |
|
2 | opnneiss | |- ( ( J e. Top /\ N e. J /\ { P } C_ N ) -> N e. ( ( nei ` J ) ` { P } ) ) |
|
3 | 1 2 | syl3an3 | |- ( ( J e. Top /\ N e. J /\ P e. N ) -> N e. ( ( nei ` J ) ` { P } ) ) |