Theorem fnafvelrn

Description: A function's value belongs to its range, analogous to fnfvelrn . (Contributed by Alexander van der Vekens, 25-May-2017)

	Ref	Expression
Assertion	fnafvelrn	⊢ ( ( 𝐹 Fn 𝐴 ∧ 𝐵 ∈ 𝐴 ) → ( 𝐹 ''' 𝐵 ) ∈ ran 𝐹 )

Proof

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