It looks like you are writing a natural deduction proof (ala Gentzen.)[/Clippy] If so, you are on the right track.
Cauchy wrote:...why are you assuming (-P v -Q)?
@j_s, take Cauchy's question seriously. In fact, turn it into two questions:
- How do you intend to discharge this assumption? Hint: What will the last two lines of your proof be, and what is the inference rule by which you arrive at the very last line? I suspect you know the answer to this question, or you would not have introduced the assumption in the first place.
- I'm guessing that what is hanging you up involves the answer to my second question: What inference rule does ¬P v ¬Q enable? Big hint: Think disjunction. Furthermore, think about how that inference rule leads to the next-to-the-last line of your proof.
Believe it or not, you've collected all the pieces. Now it's just a matter of putting them together.
ADDENDUM: The first three chapters of Logic and Proof
are a good introduction to natural deduction and section 3.1 lists the applicable inference rules. Proof formatting differs from that in the original post ("I imagine that there is a million conventions on how to format a proof...", imagines j_s, correctly), but the mechanics of inference ought to be equivalent.
"The age of the universe is 100 billion, if the units are dog years." - Sean Carroll