Consider the following premises. For all y, if y drives a car, then y is cooking. For all y, if y drives a car, then y is cooking. For all y, if y cooks, then y is driving a car. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which the fact that y drives a car does not imply that y is cooking.
 From the fact that for all y, if y cooks, then y is driving a car, and that for all y, if y drives a car, then y is cooking we can infer that for all y, y will cook if and only if y will drive a car via universal biconditional introduction. From the fact that for all y, y will cook if and only if y will drive a car we can infer that for all y, if y cooks, then y is driving a car via universal biconditional elimination. From the fact that for all y, if y cooks, then y is driving a car, and that for all y, if y drives a car, then y is cooking we can infer that for all y, y will cook if and only if y will drive a car via universal biconditional introduction. Finally, from the fact that for all y, y will cook if and only if y will drive a car we can infer that for all y, if y drives a car, then y is cooking via universal biconditional elimination, which contradicts that There is at least one y for which the fact that y drives a car does not imply that y is cooking. Therefore, the answer is no.