Consider the following premises. There is at least one x_5 for which if x_5 were excited, then x_5 is working. For all x_5, if x_5 takes a plane, then x_5 is excited. For all x_5, x_5 is fast. For all x_5, if x_5 were fast, then x_5 is taking a plane. 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 work.
 From the fact that for all x_5, if x_5 were fast, then x_5 is taking a plane, and that for all x_5, if x_5 takes a plane, then x_5 is excited we can infer that for all x_5, if x_5 were fast, then x_5 is excited via universal transitivity. From the fact that for all x_5, if x_5 were fast, then x_5 is excited, and that for all x_5, x_5 is fast we can infer that for all x_5, x_5 is excited via universal modus ponens. Finally, from the fact that there is at least one x_5 for which if x_5 were excited, then x_5 is working, and that for all x_5, x_5 is excited we can infer that there is at least one x_5 for which x_5 will work via existential modus ponens. Therefore, the answer is yes.