1. p => q Premise
2. | ¬q Assumption
3. | | p Assumption
4. | | ¬q Reiteration 3
5. | p => ¬q Implication introduction 3, 4
6. | p => q Reiteration 1
7. | ¬p Negation introduction
8. ¬q => ¬p Implication introduction 2, 8
1. ¬q ∨ ¬r Premise
2. | ¬q Assumption
3. | | q ∧ r Assumption
4. | | q And elimination 3
5. | q ∧ r => q Implication introduction 3, 4
6. | | q ∧ r Assumption
7. | | ¬q Reiterate 2
8. | q ∧ r => ¬q Implication introduction 6, 7
9. | ¬(q ∧ r) Negation introduction 5, 8
10. ¬q => ¬(q ∧ r) Implication introduction 2, 9
11. | ¬r Assumption
12. | | q ∧ r Assumption
13. | | r And elimination 12
14. | q ∧ r => r Implication introduction 12, 13
15. | | q ∧ r Assumption
16. | | ¬r Reiterate 11
17. | q ∧ r => ¬r Implication introduction 15, 16
18. | ¬(q ∧ r) Negation introduction 14, 7
19. ¬r => ¬(q ∧ r) Implication introduction 11, 18
20. ¬(q ∧ r) Or elimination 1, 10, 19