Description: Any element of a set A is the intersection of a finite subset of A . (Contributed by FL, 27-Apr-2008) (Proof shortened by Mario Carneiro, 21-Mar-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | ssfii | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex | |
|
2 | 1 | intsn | |
3 | simpl | |
|
4 | simpr | |
|
5 | 4 | snssd | |
6 | 1 | snnz | |
7 | 6 | a1i | |
8 | snfi | |
|
9 | 8 | a1i | |
10 | elfir | |
|
11 | 3 5 7 9 10 | syl13anc | |
12 | 2 11 | eqeltrrid | |
13 | 12 | ex | |
14 | 13 | ssrdv | |