Description: The intersection with a relation is a relation. (Contributed by NM, 17-Jan-2006)
Ref | Expression | ||
---|---|---|---|
Assertion | relin2 | |- ( Rel B -> Rel ( A i^i B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inss2 | |- ( A i^i B ) C_ B |
|
2 | relss | |- ( ( A i^i B ) C_ B -> ( Rel B -> Rel ( A i^i B ) ) ) |
|
3 | 1 2 | ax-mp | |- ( Rel B -> Rel ( A i^i B ) ) |