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