Consider the following premises. For all x, x will drive a car if and only if x will take a plane. For all x, x will take a plane if and only if x is a nurse. For all x, x is a nurse if and only if x will write a letter. For all x, x will not write a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x, x will not drive a car.
 From the fact that for all x, x is a nurse if and only if x will write a letter, and that for all x, x will not write a letter we can infer that for all x, x is not a nurse via universal biconditional elimination. From the fact that for all x, x will take a plane if and only if x is a nurse, and that for all x, x is not a nurse we can infer that for all x, x will not take a plane via universal biconditional elimination. Finally, from the fact that for all x, x will drive a car if and only if x will take a plane, and that for all x, x will not take a plane we can infer that for all x, x will not drive a car via universal biconditional elimination. Therefore, the answer is yes.