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