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	$$⊢C\in A\to F\left(C\right)\in B$$

Proof

Step	Hyp	Ref	Expression
1		ffvelcdmi.1	$$⊢F:A⟶B$$
2		ffvelcdm	$$⊢\left(F:A⟶B\wedge C\in A\right)\to F\left(C\right)\in B$$
3	1 2	mpan	$$⊢C\in A\to F\left(C\right)\in B$$