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