Consider the following premises. For all x_8, if x_8 were a scientist, then x_8 is a doctor. For all x_8, if x_8 were a doctor, then x_8 is a politician. For all x_8, if x_8 plays tennis, then x_8 is a scientist. There is at least one x_8 for which if x_8 were a politician, then x_8 is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which if x_8 were a doctor, then x_8 is playing tennis.
 From the fact that for all x_8, if x_8 plays tennis, then x_8 is a scientist, and that for all x_8, if x_8 were a scientist, then x_8 is a doctor we can infer that for all x_8, if x_8 plays tennis, then x_8 is a doctor via universal transitivity. Finally, from the fact that for all x_8, if x_8 were a doctor, then x_8 is a politician, and that there is at least one x_8 for which if x_8 were a politician, then x_8 is playing tennis we can infer that there is at least one x_8 for which if x_8 were a doctor, then x_8 is playing tennis via existential transitivity. Therefore, the answer is yes.