Consider the following premises. For all y_3, if y_3 cooks, then y_3 is running. For all y_3, y_3 will not go running. There is at least one y_3 for which if y_3 goes running, then y_3 is cooking. Can we infer the following from them? If we can, name the inference rule being used: For all y_3, y_3 will cook.
 From the fact that for all y_3, if y_3 cooks, then y_3 is running, and that there is at least one y_3 for which if y_3 goes running, then y_3 is cooking we can infer that there is at least one y_3 for which y_3 will cook if and only if y_3 will go running via existential biconditional introduction. Finally, from the fact that there is at least one y_3 for which y_3 will cook if and only if y_3 will go running, and that for all y_3, y_3 will not go running we can infer that there is at least one y_3 for which y_3 will not cook via existential biconditional elimination, which contradicts that For all y_3, y_3 will cook. Therefore, the answer is no.