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 ⊆ V
3		fnssres	⊢ ( ( I Fn V ∧ 𝐴 ⊆ V ) → ( I ↾ 𝐴 ) Fn 𝐴 )
4	1 2 3	mp2an	⊢ ( I ↾ 𝐴 ) Fn 𝐴