Consider the following premises. For all y, y will climb a mountain if and only if y is a writer. There is at least one y for which y will climb a mountain or y is not a writer. 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 is a writer if and only if y will climb a mountain.
 From the fact that for all y, y will climb a mountain if and only if y is a writer we can infer that for all y, if y climbs a mountain, then y is a writer via universal biconditional elimination. From the fact that there is at least one y for which y will climb a mountain or y is not a writer we can infer that there is at least one y for which if y were a writer, then y is climbing a mountain via existential rewriting. Finally, from the fact that there is at least one y for which if y were a writer, then y is climbing a mountain, and that for all y, if y climbs a mountain, then y is a writer we can infer that there is at least one y for which y is a writer if and only if y will climb a mountain via existential biconditional introduction. Therefore, the answer is yes.