Consider the following premises. For all y_1, y_1 will drive a car if and only if y_1 will take a plane. For all y_1, y_1 will not take a plane. For all y_1, if y_1 were a poet, then y_1 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_1 for which y_1 is a poet.
 From the fact that for all y_1, y_1 will drive a car if and only if y_1 will take a plane we can infer that for all y_1, if y_1 drives a car, then y_1 is taking a plane via universal biconditional elimination. From the fact that for all y_1, if y_1 were a poet, then y_1 is driving a car, and that for all y_1, if y_1 drives a car, then y_1 is taking a plane we can infer that for all y_1, if y_1 were a poet, then y_1 is taking a plane via universal transitivity. Finally, from the fact that for all y_1, if y_1 were a poet, then y_1 is taking a plane, and that for all y_1, y_1 will not take a plane we can infer that for all y_1, y_1 is not a poet via universal modus tollens, which contradicts that There is at least one y_1 for which y_1 is a poet. Therefore, the answer is no.