Metamath Proof Explorer

Theorem relin2

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 ) )

Proof

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 ) )