Consider the following premises. For all x_6, x_6 is a poet if and only if x_6 is a nurse. For all x_6, x_6 is a musician. For all x_6, x_6 will play tennis if and only if x_6 is a poet. For all x_6, if x_6 plays tennis, then x_6 is not a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is not a nurse.
 From the fact that for all x_6, if x_6 plays tennis, then x_6 is not a musician, and that for all x_6, x_6 is a musician we can infer that for all x_6, x_6 will not play tennis via universal modus tollens. From the fact that for all x_6, x_6 will play tennis if and only if x_6 is a poet, and that for all x_6, x_6 will not play tennis we can infer that for all x_6, x_6 is not a poet via universal biconditional elimination. Finally, from the fact that for all x_6, x_6 is a poet if and only if x_6 is a nurse, and that for all x_6, x_6 is not a poet we can infer that for all x_6, x_6 is not a nurse via universal biconditional elimination. Therefore, the answer is yes.