Consider the following premises. For all y_4, y_4 is rich if and only if y_4 is bored. For all y_4, y_4 is rich if and only if y_4 is bored. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_4 for which if is not true that y_4 is bored if and only if y_4 is rich.
 From the fact that for all y_4, y_4 is rich if and only if y_4 is bored we can infer that for all y_4, if y_4 were bored, then y_4 is rich via universal biconditional elimination. From the fact that for all y_4, y_4 is rich if and only if y_4 is bored we can infer that for all y_4, if y_4 were rich, then y_4 is bored via universal biconditional elimination. Finally, from the fact that for all y_4, if y_4 were bored, then y_4 is rich, and that for all y_4, if y_4 were rich, then y_4 is bored we can infer that for all y_4, y_4 is bored if and only if y_4 is rich via universal biconditional introduction, which contradicts that There is at least one y_4 for which if is not true that y_4 is bored if and only if y_4 is rich. Therefore, the answer is no.