Consider the following premises. Jennifer is sad. If Joseph were excited, then William is an office clerk. If William were rich, then Jennifer is not sad. If William were an office clerk, then Joseph is excited. For all x_14, x_14 is an office clerk if and only if x_14 is rich. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not excited.
 From the fact that for all x_14, x_14 is an office clerk if and only if x_14 is rich we can infer that William is an office clerk if and only if William is rich via universal instantiation. From the fact that if William were rich, then Jennifer is not sad, and that Jennifer is sad we can infer that William is not rich via modus tollens. From the fact that if William were an office clerk, then Joseph is excited, and that if Joseph were excited, then William is an office clerk we can infer that William is an office clerk if and only if Joseph is excited via biconditional introduction. From the fact that William is an office clerk if and only if William is rich, and that William is not rich we can infer that William is not an office clerk via biconditional elimination. Finally, from the fact that William is an office clerk if and only if Joseph is excited, and that William is not an office clerk we can infer that Joseph is not excited via biconditional elimination. Therefore, the answer is yes.