Consider the following premises. For all y, y is happy if and only if y is a writer. There is at least one y for which if y were a writer, then y is climbing a mountain. For all y, if y climbs a mountain, then y is happy. Can we infer the following from them? There is at least one y for which if y were happy, then y is a writer.
 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 happy we can infer that there is at least one y for which if y were a writer, then y is happy. From the fact that for all y, y is happy if and only if y is a writer we can infer that for all y, if y were happy, then y is a writer. From the fact that there is at least one y for which if y were a writer, then y is happy, and that for all y, if y were happy, 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 is happy. Finally, from the fact that there is at least one y for which y is a writer if and only if y is happy we can infer that there is at least one y for which if y were happy, then y is a writer. Therefore, the answer is yes.