Consider the following premises. There is at least one x_6 for which if x_6 were an astronaut, then x_6 is playing squash. For all x_6, if x_6 were an astronaut, then x_6 is driving a car. For all x_6, if x_6 drives a car, then x_6 is an astronaut. For all x_6, if x_6 plays squash, then x_6 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, if is not true that x_6 will drive a car if and only if x_6 is an astronaut.
 From the fact that there is at least one x_6 for which if x_6 were an astronaut, then x_6 is playing squash, and that for all x_6, if x_6 plays squash, then x_6 is driving a car we can infer that there is at least one x_6 for which if x_6 were an astronaut, then x_6 is driving a car via existential transitivity. Finally, from the fact that for all x_6, if x_6 drives a car, then x_6 is an astronaut, and that for all x_6, if x_6 were an astronaut, then x_6 is driving a car we can infer that for all x_6, x_6 will drive a car if and only if x_6 is an astronaut via universal biconditional introduction, which contradicts that For all x_6, if is not true that x_6 will drive a car if and only if x_6 is an astronaut. Therefore, the answer is no.