Consider the following premises. For all x_8, x_8 will cook. For all y_3, y_3 will cook if and only if y_3 is a writer. Can we infer the following from them? If we can, name the inference rule being used: James is not a writer.
 From the fact that for all x_8, x_8 will cook we can infer that James is cooking via universal instantiation. From the fact that for all y_3, y_3 will cook if and only if y_3 is a writer we can infer that James is cooking if and only if James is a writer via universal instantiation. From the fact that James is cooking if and only if James is a writer we can infer that if James cooks, then James is a writer via biconditional elimination. Finally, from the fact that if James cooks, then James is a writer, and that James is cooking we can infer that James is a writer via modus ponens, which contradicts that James is not a writer. Therefore, the answer is no.