A summary of the rules can be found [here](https://www.ocf.berkeley.edu/~brianwc/courses/logic/rulesummary.html). This is slightly different from virmaior's. 1. P(x) v Q(x) hyp 2. ~P(x) hyp 3. | P(x) hyp |------ 4. | ⊥ ⊥ Intro 2, 3 5. | Q(x) ⊥ Elim, 4 6. | Q(x) hyp |------ 7. | Q(x) Reit 6 8. Q(x) v Elim, 1, 3-5, 6-7