Negation of quantifiers and predicates

Hey guys, I have a question I answered, just want to make sure I got the correct answer or if I made any silly mistakes!

So, negate the sentence: $\displaystyle \exists x ( \forall y ( Q(x,y) \wedge ( ( \neg P(x,q) \vee Q(x,y)) \rightarrow Qy)))$

$\displaystyle \Longrightarrow \neg \exists x ( \forall y ( Q(x,y) \wedge ( ( \neg P(x,q) \vee Q(x,y)) \rightarrow Qy)))$

$\displaystyle \Longrightarrow \forall x \neg ( \forall y ( Q(x,y) \wedge ( ( \neg P(x,q) \vee Q(x,y)) \rightarrow Qy)))$

$\displaystyle \Longrightarrow \forall x ( \exists y \neg( Q(x,y) \wedge ( ( \neg P(x,q) \vee Q(x,y)) \rightarrow Qy)))$

$\displaystyle \Longrightarrow \forall x ( \exists y ( \neg Q(x,y) \vee \neg ( ( \neg P(x,q) \vee Q(x,y)) \rightarrow Qy)))$

$\displaystyle \Longrightarrow \forall x ( \exists y ( \neg Q(x,y) \vee ( ( \neg P(x,q) \vee Q(x,y)) \wedge \neg Qy)))$

now since my final answer can only involve the negation being on the $\displaystyle \neg P(x,q)$ and the $\displaystyle \neg Q(x,y)$ to get rid of the final negation on the $\displaystyle \neg Qy$ what do i need to do?

Thanks