Formal Proof - Multiple Premises

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I am trying to learn proof for my degree and in one of the exercises, it gives a proof of what seems to have multiple premises at the start. I can't seem to even figure out to start on the proof.

Premise: $A, B\to C$

Conclusion: $(A\to B)\to C$

Any help is appreciated.

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I have adopted the proof calculus from the book Logic in Computer Science: Modelling and Reasoning about Systems by Michael Huth and Mark Ryan. $$ \begin{align} &1\quad A&&\text{premise}\\ &2\quad B\to C&&\text{premise}\\ \hline &3\quad A\to B&&\text{assumption}\\ &4\quad B&&\text{$\to$e 3,1}\\ &5\quad C&&\text{$\to$e 2,4}\\ \hline &6\quad(A\to B)\to C&&\text{$\to$i 3-5} \end{align} $$