How to complete the fitch-style proof to get the desired conclusion?

Question

With this one you can use Taut Con (to implement MT, DS, DeM, if needed). Your main strategy is conditional proof/ →-Intro so you'll need a subproof.

premise 1: P → (Q → R) premise 2: P → (Q ∨ S) premise 3: P → ¬R prove: P → S

I tried this:

1. P → (Q → R) Premise

2. P → (Q ∨ S) Premise

3. P → ¬R Premise

4. Assume P Assumption

5. Assume Q Assumption

6.  P → R           → Elimination (1)
   

7.  R               → Elimination (4, 6)
   

8.  ¬R              → Elimination (3)
   

9. Q → ¬R → Introduction (5-8)

10. Assume S Assumption

11. Q ∨ S          → Elimination (2)
    

12. ¬R             → Elimination (9, 10)
    

13. S ∨ Elimination (11)

14. P → S → Introduction (4-13)

I was expecting it all to be true but it was not.