Verify the following rules and explain these rules in natural language:

5 (x ∨ y) ∧ x → y disjunctive syllogism;

6 (y → z) → ((x ∧ y) → z) strengthening the antecedent;

7 (x → y) → (x → (y ∨ z)) weakening the consequent;

8 (x → y) ∧ (x → y) → y;

9 (x → y) ∧ (x → y) → x.