Consider the following premises. For all z, if z were a janitor, then z is climbing a mountain. For all z, if z were a janitor, then z is climbing a mountain. There is at least one z for which if z climbs a mountain, then z is a janitor. Can we infer the following from them? For all z, if is not true that z is a janitor if and only if z will climb a mountain.
 From the fact that for all z, if z were a janitor, then z is climbing a mountain, and that there is at least one z for which if z climbs a mountain, then z is a janitor we can infer that there is at least one z for which z is a janitor if and only if z will climb a mountain. From the fact that there is at least one z for which z is a janitor if and only if z will climb a mountain we can infer that there is at least one z for which if z climbs a mountain, then z is a janitor. Finally, from the fact that for all z, if z were a janitor, then z is climbing a mountain, and that there is at least one z for which if z climbs a mountain, then z is a janitor we can infer that there is at least one z for which z is a janitor if and only if z will climb a mountain, which contradicts that For all z, if is not true that z is a janitor if and only if z will climb a mountain. Therefore, the answer is no.