Theorem ssres

Description: Subclass theorem for restriction. (Contributed by NM, 16-Aug-1994)

	Ref	Expression
Assertion	ssres	|- ( A C_ B -> ( A |` C ) C_ ( B |` C ) )

Proof

Step	Hyp	Ref	Expression
1		ssrin	|- ( A C_ B -> ( A i^i ( C X. _V ) ) C_ ( B i^i ( C X. _V ) ) )
2		df-res	|- ( A |` C ) = ( A i^i ( C X. _V ) )
3		df-res	|- ( B |` C ) = ( B i^i ( C X. _V ) )
4	1 2 3	3sstr4g	|- ( A C_ B -> ( A |` C ) C_ ( B |` C ) )