Description: The intersection of a class containing the empty set is empty. (Contributed by NM, 24-Apr-2004)
Ref | Expression | ||
---|---|---|---|
Assertion | int0el | |- ( (/) e. A -> |^| A = (/) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | intss1 | |- ( (/) e. A -> |^| A C_ (/) ) |
|
2 | 0ss | |- (/) C_ |^| A |
|
3 | 2 | a1i | |- ( (/) e. A -> (/) C_ |^| A ) |
4 | 1 3 | eqssd | |- ( (/) e. A -> |^| A = (/) ) |