Natural Deduction Proof $\neg(P \to Q) \vdash Q \to P$

Question

I am trying to answer Question 3(e) in Exercise 1.2 of Huth and Ryan's Logic in Computer Science book for revision and I am stuck on it. The question asks you to prove the validity of the following sequent:

$\neg(P \to Q) \vdash Q \to P$

Any help would be appreciated.

Answer 1

Following the nomenclature as demonstrated in the solutions of your book (this particular question is not included, so this is not plagiarism):

1. ¬(P→Q)  assumption
  2. Q     assumption
    3. P   assumption
    4. Q   copy 2
  5. P→Q   →i 3-4
  6. ⊥     ¬e 5 1
  7. P     ⊥e 6
8. Q→P     →i 2-7

Where it used boxes, I used indentation. I won't draw boxes. I simply refuse to do so.