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