Proving De Morgan's Law with Natural Deduction

In the second part lines 2 and 7 are redundant, instead assume line 3.

Edit: As noticed by @GitGud, in the first part, line 6 must be $\neg\neg p \ (\neg I)$. So you need to add another line to get $p$ by $(\neg\neg E)$. Similar correction for line 10.