Description: An empty indexed union is empty. (Contributed by NM, 4-Dec-2004) (Proof shortened by Andrew Salmon, 25-Jul-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | 0iun | |- U_ x e. (/) A = (/) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rex0 | |- -. E. x e. (/) y e. A |
|
2 | eliun | |- ( y e. U_ x e. (/) A <-> E. x e. (/) y e. A ) |
|
3 | 1 2 | mtbir | |- -. y e. U_ x e. (/) A |
4 | 3 | nel0 | |- U_ x e. (/) A = (/) |