Theorem ffvelcdmi

Description: A function's value belongs to its codomain. (Contributed by NM, 6-Apr-2005)

	Ref	Expression
Hypothesis	ffvelcdmi.1	⊢ 𝐹 : 𝐴 ⟶ 𝐵
Assertion	ffvelcdmi	⊢ ( 𝐶 ∈ 𝐴 → ( 𝐹 ‘ 𝐶 ) ∈ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		ffvelcdmi.1	⊢ 𝐹 : 𝐴 ⟶ 𝐵
2		ffvelcdm	⊢ ( ( 𝐹 : 𝐴 ⟶ 𝐵 ∧ 𝐶 ∈ 𝐴 ) → ( 𝐹 ‘ 𝐶 ) ∈ 𝐵 )
3	1 2	mpan	⊢ ( 𝐶 ∈ 𝐴 → ( 𝐹 ‘ 𝐶 ) ∈ 𝐵 )