Consider the following premises. For all y, y will make tea or y is not sad. There is at least one y for which if y makes tea, then y is sad. For all y, if y makes tea, then y is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which y will make tea if and only if y is sad.
 From the fact that for all y, y will make tea or y is not sad we can infer that for all y, if y were sad, then y is making tea via universal rewriting. From the fact that for all y, if y makes tea, then y is sad, and that for all y, if y were sad, then y is making tea we can infer that for all y, y will make tea if and only if y is sad via universal biconditional introduction. From the fact that for all y, y will make tea if and only if y is sad we can infer that for all y, if y were sad, then y is making tea via universal biconditional elimination. Finally, from the fact that there is at least one y for which if y makes tea, then y is sad, and that for all y, if y were sad, then y is making tea we can infer that there is at least one y for which y will make tea if and only if y is sad via existential biconditional introduction. Therefore, the answer is yes.