Description: If a set is closed under finite intersection, then it is a basis for a topology. (Contributed by Jeff Madsen, 2-Sep-2009)
Ref | Expression | ||
---|---|---|---|
Assertion | fiinbas | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid | |
|
2 | eleq2 | |
|
3 | sseq1 | |
|
4 | 2 3 | anbi12d | |
5 | 4 | rspcev | |
6 | 1 5 | mpanr2 | |
7 | 6 | ralrimiva | |
8 | 7 | a1i | |
9 | 8 | ralimdv | |
10 | 9 | ralimdv | |
11 | isbasis2g | |
|
12 | 10 11 | sylibrd | |
13 | 12 | imp | |