Theorem ffvelrnda

Description: A function's value belongs to its codomain. (Contributed by Mario Carneiro, 29-Dec-2016)

	Ref	Expression
Hypothesis	ffvelrnd.1	$$⊢\phi \to F:A⟶B$$
Assertion	ffvelrnda	$$⊢\left(\phi \wedge C\in A\right)\to F\left(C\right)\in B$$

Proof

Step	Hyp	Ref	Expression
1		ffvelrnd.1	$$⊢\phi \to F:A⟶B$$
2		ffvelrn	$$⊢\left(F:A⟶B\wedge C\in A\right)\to F\left(C\right)\in B$$
3	1 2	sylan	$$⊢\left(\phi \wedge C\in A\right)\to F\left(C\right)\in B$$