Consider the following premises. For all y, y will not work. There is at least one y for which y is a poet if and only if y will work. Can we infer the following from them? If we can, name the inference rule being used: For all y, y is a poet.
 From the fact that there is at least one y for which y is a poet if and only if y will work we can infer that there is at least one y for which if y were a poet, then y is working via existential biconditional elimination. Finally, from the fact that there is at least one y for which if y were a poet, then y is working, and that for all y, y will not work we can infer that there is at least one y for which y is not a poet via existential modus tollens, which contradicts that For all y, y is a poet. Therefore, the answer is no.