Consider the following premises. For all y, if y listens to a song, then y is driving a car. For all y, y will make tea or y will not drive a car. For all y, if y makes tea, then y is playing squash. For all y, if y plays squash, then y is making tea. Can we infer the following from them? If we can, name the inference rule being used: For all y, if y listens to a song, then y is playing squash.
 From the fact that for all y, if y plays squash, then y is making tea, and that for all y, if y makes tea, then y is playing squash we can infer that for all y, y will play squash if and only if y will make tea via universal biconditional introduction. From the fact that for all y, y will play squash if and only if y will make tea we can infer that for all y, if y makes tea, then y is playing squash via universal biconditional elimination. From the fact that for all y, y will make tea or y will not drive a car we can infer that for all y, if y drives a car, then y is making tea via universal rewriting. From the fact that for all y, if y listens to a song, then y is driving a car, and that for all y, if y drives a car, then y is making tea we can infer that for all y, if y listens to a song, then y is making tea via universal transitivity. Finally, from the fact that for all y, if y listens to a song, then y is making tea, and that for all y, if y makes tea, then y is playing squash we can infer that for all y, if y listens to a song, then y is playing squash via universal transitivity. Therefore, the answer is yes.