It's me again, lol.

Find a valid conclusion to the argument given bwlow in symbolic form. Justify your answer.

~p (p^ ~q) ------ premise 1

q --> r --------- premise 2

~ r -------------- premise 3

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therefore, ?

Here is what I did last night,

1. ~r PIII

2. ~r-->~q PII, contrapositive

3. ~q 1,2,detachment

4. ~p v q PI, DeMorgan's Laws

5. ~p 3,4,disjunctive syllogism

therefore, ~p. not sure if this is right or my work is right, thanks in advance.