Formal Deduction (logic) Question: $\lnot C, (B \to \lnot C) \to A \vdash (A \to C) \to F$ I've been stuck on this question for around two hours now. 
I'm trying to prove that:
$\lnot C, \ (B \to \lnot C)\to A \vdash (A \to C)\to F $
I'm trying to get my second last step to be:
$\lnot C, \ (B \to \lnot C)\to A, \ A \to C \vdash F $,
but I have no idea how to get started. I'm not sure what I can start off with, especially due to the $(B \to \lnot C)\to A)$ part.
I'm allowed to use 11 rules of formal deducibility/deduction. 
If anyone can help me get started, or give me some hints, I would be extremely thankful!

You can show that $((B\to \neg C)\to A) \iff ((B\land C)\lor A)$.
Now adding $A \to C$ to the hypotheses and using disjunction of cases:
\begin{array}{l}
     A \\
     A \to C \\
    \hline
     C 
\end{array}
Which considering $\neg C$ is absurd. Also:
\begin{array}{l}
     B\land C \\
    \hline
     C 
\end{array}
which is again absurd.
So we've shown that $A\to C$ is false, so $(A\to C)\to F$ is true regardless of $F$.
