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