Consider the following premises. For all y, if y drives a car, then y is a writer. For all x_3, x_3 will drive a car. If Barbara were a writer, then Elisabeth is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not an astronaut.
 From the fact that for all x_3, x_3 will drive a car we can infer that Barbara is driving a car via universal instantiation. From the fact that for all y, if y drives a car, then y is a writer we can infer that if Barbara drives a car, then Barbara is a writer via universal instantiation. From the fact that if Barbara drives a car, then Barbara is a writer, and that Barbara is driving a car we can infer that Barbara is a writer via modus ponens. Finally, from the fact that if Barbara were a writer, then Elisabeth is an astronaut, and that Barbara is a writer we can infer that Elisabeth is an astronaut via modus ponens, which contradicts that Elisabeth is not an astronaut. Therefore, the answer is no.