Consider the following premises. For all x_7, x_7 will cook if and only if x_7 is an office clerk. For all x_7, x_7 is a mechanic if and only if x_7 will cook. For all x_7, x_7 is not a mechanic. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is not an office clerk.
 From the fact that for all x_7, x_7 is a mechanic if and only if x_7 will cook, and that for all x_7, x_7 is not a mechanic we can infer that for all x_7, x_7 will not cook via universal biconditional elimination. From the fact that for all x_7, x_7 will cook if and only if x_7 is an office clerk we can infer that for all x_7, if x_7 were an office clerk, then x_7 is cooking via universal biconditional elimination. Finally, from the fact that for all x_7, if x_7 were an office clerk, then x_7 is cooking, and that for all x_7, x_7 will not cook we can infer that for all x_7, x_7 is not an office clerk via universal modus tollens. Therefore, the answer is yes.