Theorem fnssres

Description: Restriction of a function with a subclass of its domain. (Contributed by NM, 2-Aug-1994)

	Ref	Expression
Assertion	fnssres	⊢ ( ( 𝐹 Fn 𝐴 ∧ 𝐵 ⊆ 𝐴 ) → ( 𝐹 ↾ 𝐵 ) Fn 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		fnssresb	⊢ ( 𝐹 Fn 𝐴 → ( ( 𝐹 ↾ 𝐵 ) Fn 𝐵 ↔ 𝐵 ⊆ 𝐴 ) )
2	1	biimpar	⊢ ( ( 𝐹 Fn 𝐴 ∧ 𝐵 ⊆ 𝐴 ) → ( 𝐹 ↾ 𝐵 ) Fn 𝐵 )