Consider the following premises. For all x_13, x_13 will make tea or x_13 will not drive a car. There is at least one x_13 for which x_13 will drive a car. For all x_13, x_13 will work. 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 work.
 From the fact that for all x_13, x_13 will make tea or x_13 will not drive a car we can infer that for all x_13, if x_13 drives a car, then x_13 is making tea via universal rewriting. From the fact that for all x_13, if x_13 drives a car, then x_13 is making tea, and that there is at least one x_13 for which x_13 will drive a car we can infer that there is at least one x_13 for which x_13 will make tea via existential modus ponens. From the fact that there is at least one x_13 for which x_13 will make tea, and that for all x_13, x_13 will work we can infer that there is at least one x_13 for which x_13 will make tea and x_13 will work via existential conjunction. Finally, from the fact that there is at least one x_13 for which x_13 will make tea and x_13 will work we can infer that there is at least one x_13 for which x_13 will work via existential simplification. Therefore, the answer is yes.