Metamath Proof Explorer

Theorem reldif

Description: A difference cutting down a relation is a relation. (Contributed by NM, 31-Mar-1998)

Ref Expression
Assertion reldif 
|- ( Rel A -> Rel ( A \ B ) )

Proof

Step Hyp Ref Expression
1 difss 
 |-  ( A \ B ) C_ A
2 relss 
 |-  ( ( A \ B ) C_ A -> ( Rel A -> Rel ( A \ B ) ) )
3 1 2 ax-mp 
 |-  ( Rel A -> Rel ( A \ B ) )