Natural deduction proof: {A → B, B → (C & D), ¬C v ¬D} ⊢ ¬A

Question

Prove using natural deduction: $ {A → B, B → (C \land D), ¬C \vee ¬D} ⊢ ¬A$

Our work (so far):

$1- A → B$

$2- B → (C \land D)$

$3- ¬¬A$

$4- A$

$5- B$ (from 1,4) $→E$

$6- B$

$7- C \land D$ (from 2,6) $→E$

This is where I've been for the past 6 hours. Help me out if you can. Thanks.

Answer 1

Get the contra-positives of 1&2 as $\neg B\rightarrow \neg A$ and $\neg C \,\,V\neg D \rightarrow \neg B$. Use $\neg C \,\,V\neg D \rightarrow \neg B, \,\,\,\, \neg B \rightarrow \neg A$ and the result follows.