Natural Deduction introduction of implication

If we want to derive $A\to B$ from some premises, then we must show that these premises together with $A$ imply $B$. ?

$$\frac{\text{premises}}{A\to B},\text{if }\frac{\text{premises},A}{B}(\to I)$$

The proof that $B$ follows from the addition of $A$ to premises is done in a separate subcomputation box.