Consider the following premises. If Thomas drives a car, then Joseph is excited. If Joseph were excited, then Thomas is an astronaut. For all z, if z were an astronaut, then z is driving a car. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Thomas is driving a car if and only if Thomas is an astronaut.
 From the fact that for all z, if z were an astronaut, then z is driving a car we can infer that if Thomas were an astronaut, then Thomas is driving a car via universal instantiation. From the fact that if Thomas drives a car, then Joseph is excited, and that if Joseph were excited, then Thomas is an astronaut we can infer that if Thomas drives a car, then Thomas is an astronaut via transitivity. Finally, from the fact that if Thomas drives a car, then Thomas is an astronaut, and that if Thomas were an astronaut, then Thomas is driving a car we can infer that Thomas is driving a car if and only if Thomas is an astronaut via biconditional introduction, which contradicts that If is not true that Thomas is driving a car if and only if Thomas is an astronaut. Therefore, the answer is no.