Consider the following premises. For all y, if y were happy, then y is taking a plane. There is at least one y for which if y were poor, then y is playing squash. For all y, y will play squash if and only if y is happy. For all y, y is poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which y will take a plane.
 From the fact that for all y, y will play squash if and only if y is happy we can infer that for all y, if y plays squash, then y is happy via universal biconditional elimination. From the fact that for all y, if y plays squash, then y is happy, and that for all y, if y were happy, then y is taking a plane we can infer that for all y, if y plays squash, then y is taking a plane via universal transitivity. From the fact that there is at least one y for which if y were poor, then y is playing squash, and that for all y, y is poor we can infer that there is at least one y for which y will play squash via existential modus ponens. Finally, from the fact that for all y, if y plays squash, then y is taking a plane, and that there is at least one y for which y will play squash we can infer that there is at least one y for which y will take a plane via existential modus ponens. Therefore, the answer is yes.