Formal proof of $P\to Q, (P\to Q)\to (T\to S), \neg Q, P\lor T\vdash S$

Question

This is an example exam question that I'm wondering if I did right? We weren't given an answer key, so I'm checking to make sure I'm comprehending the material and if my answer is correct?

Premises: P $\Rightarrow$ Q, (P $\Rightarrow$ Q) $\Rightarrow$ (T $\Rightarrow$ S), $\lnot$Q, P $\lor$ T

Conclusion: S

My answer:

1. P $\Rightarrow$ Q: Given

2. (P $\Rightarrow$ Q) $\Rightarrow$ (T $\Rightarrow$ S): Given

3. $\lnot$Q: Given

4. P $\lor$ T: Given

5. T $\Rightarrow$ S: Modus Ponens 1 and 2

6. $\lnot$P: Modus Tollens 1 and 3

7. T: Disjunctive Syllogism 4 and 6

8. S: Modus Ponens 5 and 7

Answer 1

The proof seems fine. This is a community wiki post so that the question is not marked as unanswered.