Theorem fnfvelrnd

Description: A function's value belongs to its range. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypotheses	fnfvelrnd.1	⊢ ( 𝜑 → 𝐹 Fn 𝐴 )
	fnfvelrnd.2	⊢ ( 𝜑 → 𝐵 ∈ 𝐴 )
Assertion	fnfvelrnd	⊢ ( 𝜑 → ( 𝐹 ‘ 𝐵 ) ∈ ran 𝐹 )

Proof

Step	Hyp	Ref	Expression
1		fnfvelrnd.1	⊢ ( 𝜑 → 𝐹 Fn 𝐴 )
2		fnfvelrnd.2	⊢ ( 𝜑 → 𝐵 ∈ 𝐴 )
3		fnfvelrn	⊢ ( ( 𝐹 Fn 𝐴 ∧ 𝐵 ∈ 𝐴 ) → ( 𝐹 ‘ 𝐵 ) ∈ ran 𝐹 )
4	1 2 3	syl2anc	⊢ ( 𝜑 → ( 𝐹 ‘ 𝐵 ) ∈ ran 𝐹 )