Theorem fnresi

Description: The restricted identity relation is a function on the restricting class. (Contributed by NM, 27-Aug-2004) (Proof shortened by BJ, 27-Dec-2023)

	Ref	Expression
Assertion	fnresi	|- ( _I |` A ) Fn A

Proof

Step	Hyp	Ref	Expression
1		idfn	|- _I Fn _V
2		ssv	|- A C_ _V
3		fnssres	|- ( ( _I Fn _V /\ A C_ _V ) -> ( _I |` A ) Fn A )
4	1 2 3	mp2an	|- ( _I |` A ) Fn A