Consider the following premises. For all y, if y makes tea, then y is climbing a mountain. There is at least one y for which if y climbs a mountain, then y is making tea. For all y, if y climbs a mountain, then y is making tea. 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 climb a mountain if and only if y will make tea.
 From the fact that for all y, if y makes tea, then y is climbing a mountain, and that there is at least one y for which if y climbs a mountain, 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 will climb a mountain via existential biconditional introduction. From the fact that there is at least one y for which y will make tea if and only if y will climb a mountain we can infer that there is at least one y for which if y makes tea, then y is climbing a mountain via existential biconditional elimination. Finally, from the fact that for all y, if y climbs a mountain, then y is making tea, and that there is at least one y for which if y makes tea, then y is climbing a mountain we can infer that there is at least one y for which y will climb a mountain if and only if y will make tea via existential biconditional introduction. Therefore, the answer is yes.