Consider the following premises. For all x_5, x_5 will play tennis. There is at least one x_5 for which x_5 is a writer. For all x_5, if x_5 were a writer, then x_5 is a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will play tennis.
 From the fact that for all x_5, if x_5 were a writer, then x_5 is a taxi driver, and that there is at least one x_5 for which x_5 is a writer we can infer that there is at least one x_5 for which x_5 is a taxi driver via existential modus ponens. From the fact that there is at least one x_5 for which x_5 is a taxi driver, and that for all x_5, x_5 will play tennis we can infer that there is at least one x_5 for which x_5 is a taxi driver and x_5 will play tennis via existential conjunction. Finally, from the fact that there is at least one x_5 for which x_5 is a taxi driver and x_5 will play tennis we can infer that there is at least one x_5 for which x_5 will play tennis via existential simplification. Therefore, the answer is yes.