Consider the following premises. For all x_13, if x_13 were an electrician, then x_13 is a doctor. For all x_13, x_13 will play tennis or x_13 is not a doctor. There is at least one x_13 for which x_13 is an electrician or x_13 is an office clerk. For all x_13, if x_13 were an office clerk, then x_13 is a doctor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_13 for which x_13 will play tennis.
 From the fact that for all x_13, if x_13 were an electrician, then x_13 is a doctor, that for all x_13, if x_13 were an office clerk, then x_13 is a doctor, and that there is at least one x_13 for which x_13 is an electrician or x_13 is an office clerk we can infer that there is at least one x_13 for which x_13 is a doctor via existential disjunction elimination. From the fact that for all x_13, x_13 will play tennis or x_13 is not a doctor we can infer that for all x_13, if x_13 were a doctor, then x_13 is playing tennis via universal rewriting. Finally, from the fact that for all x_13, if x_13 were a doctor, then x_13 is playing tennis, and that there is at least one x_13 for which x_13 is a doctor we can infer that there is at least one x_13 for which x_13 will play tennis via existential modus ponens. Therefore, the answer is yes.