Fitch-Style Proof Hi I'm having trouble solving a Fitch Style Proof and I was hoping someone would be able to help me.
Premises:

$A \land (B \lor C)$
  $B \to D$
  $C \to E$

Goal: $\neg E \to D$
Thank You

You should be able to transform the following in a formal proof.
Assume $\neg E$.
Prove $B\lor \neg B$ with the intent to use $\lor$-$\text{Elim}$.
If $B$ holds, then use $\to$-$\text{Elim}$ on the premise $B\to D$ to conclude $D$.
Suppose $\neg B$ holds. Use $\land$-$\text{Elim}$ on the first premise to get $B\lor C$. You will want to use $\lor$-$\text{Elim}$ on $B\lor C$. If $B$ holds you can get $D$ in two ways, choose one of them. If $C$ holds, eliminate $\to$ on the premise $C\to E$ to get $E$ and a consequently a contradiction, thus getting $D$ with $\bot$-$\text{Elim}$. Eliminating the disjunction $B\lor C$ gives you $D$.
Eliminating the disjunction $B\lor \neg B$ yields $D$.
Finish off.
You can find the proof hidden in the grey area below.



