Hi guys!

I need to prove De Morgan's law for a logic class. My friend and I were successful with the first theorem:

~(P^Q)<=>~Pv~Q

1. ~(PvQ) |P(1)
2. P |A(2)
3. PvQ |(vIntro) 2 (2)
4. falsum |(~Elim) 1,3 (1,2)
5. ~P |(~Intro) 2,4 (1,2)
6. Q |A(6)
7. PvQ |(vIntro) 6 (6)
8. falsum |(~Elim) 1,7 (1,6)
9. ~Q |(~Intro) 6,8 (1,6)
10. ~P^~Q |(^Intro) 5,9 (1)

I've been trying to solve the second theorem but I think that I'm stuck. Can you help me prove ~(pvq)<=>~p^~q?

Thanks!!!