Description: The intersection with a relation is a relation. (Contributed by NM, 16-Aug-1994)
Ref | Expression | ||
---|---|---|---|
Assertion | relin1 | |- ( Rel A -> Rel ( A i^i B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inss1 | |- ( A i^i B ) C_ A |
|
2 | relss | |- ( ( A i^i B ) C_ A -> ( Rel A -> Rel ( A i^i B ) ) ) |
|
3 | 1 2 | ax-mp | |- ( Rel A -> Rel ( A i^i B ) ) |