Consider the following premises. There is at least one y for which y will not play tennis. For all y, if y plays tennis, then y is a doctor. For all y, if y were a doctor, then y is playing tennis. For all y, y is a musician if and only if y is a doctor. Can we infer the following from them? If we can, name the inference rule being used: For all y, y is a musician.
 From the fact that for all y, if y were a doctor, then y is playing tennis, and that for all y, if y plays tennis, then y is a doctor we can infer that for all y, y is a doctor if and only if y will play tennis via universal biconditional introduction. From the fact that for all y, y is a doctor if and only if y will play tennis, and that there is at least one y for which y will not play tennis we can infer that there is at least one y for which y is not a doctor via existential biconditional elimination. Finally, from the fact that for all y, y is a musician if and only if y is a doctor, and that there is at least one y for which y is not a doctor we can infer that there is at least one y for which y is not a musician via existential biconditional elimination, which contradicts that For all y, y is a musician. Therefore, the answer is no.