Description: A nonempty ball implies that the radius is positive. (Contributed by NM, 11-Mar-2007) (Revised by Mario Carneiro, 23-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | blgt0 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0xr | |
|
2 | 1 | a1i | |
3 | simpl1 | |
|
4 | simpl2 | |
|
5 | elbl | |
|
6 | 5 | simprbda | |
7 | xmetcl | |
|
8 | 3 4 6 7 | syl3anc | |
9 | simpl3 | |
|
10 | xmetge0 | |
|
11 | 3 4 6 10 | syl3anc | |
12 | 5 | simplbda | |
13 | 2 8 9 11 12 | xrlelttrd | |