Description: The intersection of two sets is finite if one of them is. (Contributed by Thierry Arnoux, 14-Feb-2017)
Ref | Expression | ||
---|---|---|---|
Assertion | infi | |- ( A e. Fin -> ( A i^i B ) e. Fin ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inss1 | |- ( A i^i B ) C_ A |
|
2 | ssfi | |- ( ( A e. Fin /\ ( A i^i B ) C_ A ) -> ( A i^i B ) e. Fin ) |
|
3 | 1 2 | mpan2 | |- ( A e. Fin -> ( A i^i B ) e. Fin ) |