Description: A set strictly dominates the empty set iff it is not empty. (Contributed by NM, 29-Jul-2004)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | 0sdom.1 | |- A e. _V |
|
| Assertion | 0sdom | |- ( (/) ~< A <-> A =/= (/) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 0sdom.1 | |- A e. _V |
|
| 2 | 0sdomg | |- ( A e. _V -> ( (/) ~< A <-> A =/= (/) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( (/) ~< A <-> A =/= (/) ) |