Theorem fnssresd

Description: Restriction of a function to a subclass of its domain. (Contributed by Glauco Siliprandi, 5-Feb-2022)

	Ref	Expression
Hypotheses	fnssresd.1	⊢ ( 𝜑 → 𝐹 Fn 𝐴 )
	fnssresd.2	⊢ ( 𝜑 → 𝐵 ⊆ 𝐴 )
Assertion	fnssresd	⊢ ( 𝜑 → ( 𝐹 ↾ 𝐵 ) Fn 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		fnssresd.1	⊢ ( 𝜑 → 𝐹 Fn 𝐴 )
2		fnssresd.2	⊢ ( 𝜑 → 𝐵 ⊆ 𝐴 )
3		fnssres	⊢ ( ( 𝐹 Fn 𝐴 ∧ 𝐵 ⊆ 𝐴 ) → ( 𝐹 ↾ 𝐵 ) Fn 𝐵 )
4	1 2 3	syl2anc	⊢ ( 𝜑 → ( 𝐹 ↾ 𝐵 ) Fn 𝐵 )