Consider the following premises. For all x, x will play tennis if and only if x is a poet. There is at least one x for which x will not cook. For all x, x will cook if and only if x will play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x is not a poet.
 From the fact that for all x, x will cook if and only if x will play tennis, and that there is at least one x for which x will not cook we can infer that there is at least one x for which x will not play tennis via existential biconditional elimination. Finally, from the fact that for all x, x will play tennis if and only if x is a poet, and that there is at least one x for which x will not play tennis we can infer that there is at least one x for which x is not a poet via existential biconditional elimination. Therefore, the answer is yes.