Description: Reverse closure for the limit point predicate. (Contributed by Mario Carneiro, 9-Apr-2015) (Revised by Stefan O'Rear, 9-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | flimtop | |- ( A e. ( J fLim F ) -> J e. Top ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | |- U. J = U. J |
|
2 | 1 | elflim2 | |- ( A e. ( J fLim F ) <-> ( ( J e. Top /\ F e. U. ran Fil /\ F C_ ~P U. J ) /\ ( A e. U. J /\ ( ( nei ` J ) ` { A } ) C_ F ) ) ) |
3 | 2 | simplbi | |- ( A e. ( J fLim F ) -> ( J e. Top /\ F e. U. ran Fil /\ F C_ ~P U. J ) ) |
4 | 3 | simp1d | |- ( A e. ( J fLim F ) -> J e. Top ) |