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 =/= (/) ) |