Theorem fnfvelrn

Description: A function's value belongs to its range. (Contributed by NM, 15-Oct-1996)

	Ref	Expression
Assertion	fnfvelrn	⊢ ( ( 𝐹 Fn 𝐴 ∧ 𝐵 ∈ 𝐴 ) → ( 𝐹 ‘ 𝐵 ) ∈ ran 𝐹 )

Proof

Step	Hyp	Ref	Expression
1		fvelrn	⊢ ( ( Fun 𝐹 ∧ 𝐵 ∈ dom 𝐹 ) → ( 𝐹 ‘ 𝐵 ) ∈ ran 𝐹 )
2	1	funfni	⊢ ( ( 𝐹 Fn 𝐴 ∧ 𝐵 ∈ 𝐴 ) → ( 𝐹 ‘ 𝐵 ) ∈ ran 𝐹 )