Consider the following premises. There is at least one x_4 for which x_4 will cook if and only if x_4 will take a plane. For all x_4, x_4 will cook. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 will not take a plane.
 From the fact that there is at least one x_4 for which x_4 will cook if and only if x_4 will take a plane we can infer that there is at least one x_4 for which if x_4 cooks, then x_4 is taking a plane via existential biconditional elimination. Finally, from the fact that there is at least one x_4 for which if x_4 cooks, then x_4 is taking a plane, and that for all x_4, x_4 will cook we can infer that there is at least one x_4 for which x_4 will take a plane via existential modus ponens, which contradicts that For all x_4, x_4 will not take a plane. Therefore, the answer is no.