Consider the following premises. For all x_7, x_7 will not play tennis. For all x_7, if x_7 cooks, then x_7 is driving a car. There is at least one x_7 for which x_7 will drive a car if and only if x_7 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will cook.
 From the fact that there is at least one x_7 for which x_7 will drive a car if and only if x_7 will play tennis, and that for all x_7, x_7 will not play tennis we can infer that there is at least one x_7 for which x_7 will not drive a car via existential biconditional elimination. Finally, from the fact that for all x_7, if x_7 cooks, then x_7 is driving a car, and that there is at least one x_7 for which x_7 will not drive a car we can infer that there is at least one x_7 for which x_7 will not cook via existential modus tollens, which contradicts that For all x_7, x_7 will cook. Therefore, the answer is no.