Consider the following premises. For all z, z will drink water if and only if z is poor. For all z, if z were a poet, then z is poor. There is at least one z for which z is a poet or z will drink water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which z is poor or z will play tennis.
 From the fact that for all z, z will drink water if and only if z is poor we can infer that for all z, if z drinks water, then z is poor via universal biconditional elimination. From the fact that for all z, if z were a poet, then z is poor, that for all z, if z drinks water, then z is poor, and that there is at least one z for which z is a poet or z will drink water we can infer that there is at least one z for which z is poor via existential disjunction elimination. Finally, from the fact that there is at least one z for which z is poor we can infer that there is at least one z for which z is poor or z will play tennis via existential addition. Therefore, the answer is yes.