Proving tautology

Question

Trying to prove if this statement is a tautology:

$\neg (p\to q) \to p$

I can simplify the left hand side $\neg (p\to q)$ to $p\land \neg q$, but once I get there I'm stuck.

Answer 1

Apply the equivalence of implication twice, then commute and associate so that you can apply identity rules.

$$\neg(p\to q)\to p \\= (p\to q) \vee p \\ = (\neg p \vee q)\vee p \\ \vdots$$

Answer 2

HINT (first 2 lines):

1. Suppose $\neg[P\implies Q]$

2. $\neg\neg[P\land \neg Q]$ (from 1)