Theorem ffvelrnd

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

	Ref	Expression
Hypotheses	ffvelrnd.1	$$⊢\phi \to F:A⟶B$$
	ffvelrnd.2	$$⊢\phi \to C\in A$$
Assertion	ffvelrnd	$$⊢\phi \to F\left(C\right)\in B$$

Proof

Step	Hyp	Ref	Expression
1		ffvelrnd.1	$$⊢\phi \to F:A⟶B$$
2		ffvelrnd.2	$$⊢\phi \to C\in A$$
3	1	ffvelrnda	$$⊢\left(\phi \wedge C\in A\right)\to F\left(C\right)\in B$$
4	2 3	mpdan	$$⊢\phi \to F\left(C\right)\in B$$