Consider the following premises. For all x_10, if x_10 drives a car, then x_10 is sleeping. For all x_10, x_10 will not sleep. For all x_10, if x_10 sleeps, then x_10 is driving a car. If it is cold, then Thomas is driving a car. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that for all x_10, if x_10 drives a car, then x_10 is sleeping, and that for all x_10, if x_10 sleeps, then x_10 is driving a car we can infer that for all x_10, x_10 will drive a car if and only if x_10 will sleep via universal biconditional introduction. From the fact that for all x_10, x_10 will drive a car if and only if x_10 will sleep, and that for all x_10, x_10 will not sleep we can infer that for all x_10, x_10 will not drive a car via universal biconditional elimination. From the fact that for all x_10, x_10 will not drive a car we can infer that Thomas is not driving a car via universal instantiation. Finally, from the fact that if it is cold, then Thomas is driving a car, and that Thomas is not driving a car we can infer that it is not cold via modus tollens. Therefore, the answer is yes.