Using only the rules of inference to derive a conditional statement.

Question

I have this question: P → ¬¬Q ⊢ ¬Q → ¬P I have these steps for proof:

1. (1) P → ¬¬Q Premise

2. (2) ¬Q Premise

1,2. (3) ¬P (1,2 Modus Tollens)

1. (4) ¬Q → ¬P (2,3 CP)

Is this correct or do I need to do a double negation at some point? The only applicable rules we're allowed to use are modus tollens, modus ponuns, double negation, and CP.