Consider the following premises. Joseph is an astronaut if and only if it is not raining. If it rains, then David is not a writer. For all x_3, x_3 is a writer. Can we infer the following from them? If we can, name the inference rule being used: Joseph is an astronaut.
 From the fact that for all x_3, x_3 is a writer we can infer that David is a writer via universal instantiation. From the fact that if it rains, then David is not a writer, and that David is a writer we can infer that it is not raining via modus tollens. From the fact that Joseph is an astronaut if and only if it is not raining we can infer that if it doesn't rain, then Joseph is an astronaut via biconditional elimination. Finally, from the fact that if it doesn't rain, then Joseph is an astronaut, and that it is not raining we can infer that Joseph is an astronaut via modus ponens. Therefore, the answer is yes.