Metamath Proof Explorer

Theorem relin1

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 ) )

Proof

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 ) )