Description: The singleton of the empty set is a topology on the empty set. (Contributed by Mario Carneiro, 13-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | sn0topon | |- { (/) } e. ( TopOn ` (/) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pw0 | |- ~P (/) = { (/) } |
|
2 | 0ex | |- (/) e. _V |
|
3 | distopon | |- ( (/) e. _V -> ~P (/) e. ( TopOn ` (/) ) ) |
|
4 | 2 3 | ax-mp | |- ~P (/) e. ( TopOn ` (/) ) |
5 | 1 4 | eqeltrri | |- { (/) } e. ( TopOn ` (/) ) |