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