Consider the following premises. For all x_6, x_6 will work if and only if x_6 will drive a car. For all x_6, x_6 is an astronaut or x_6 will not drive a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, if x_6 works, then x_6 is an astronaut.
 From the fact that for all x_6, x_6 is an astronaut or x_6 will not drive a car we can infer that for all x_6, if x_6 drives a car, then x_6 is an astronaut via universal rewriting. From the fact that for all x_6, x_6 will work if and only if x_6 will drive a car we can infer that for all x_6, if x_6 works, then x_6 is driving a car via universal biconditional elimination. Finally, from the fact that for all x_6, if x_6 works, then x_6 is driving a car, and that for all x_6, if x_6 drives a car, then x_6 is an astronaut we can infer that for all x_6, if x_6 works, then x_6 is an astronaut via universal transitivity. Therefore, the answer is yes.