Description: No set is a proper subset of the empty set. (Contributed by NM, 17-Jun-1998) (Proof shortened by Andrew Salmon, 26-Jun-2011) (Proof shortened by JJ, 14-Jul-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | npss0 | |- -. A C. (/) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 0ss | |- (/) C_ A |
|
| 2 | ssnpss | |- ( (/) C_ A -> -. A C. (/) ) |
|
| 3 | 1 2 | ax-mp | |- -. A C. (/) |