Consider the following premises. For all z_3, z_3 will listen to a song if and only if z_3 will climb a mountain. For all z_3, if z_3 listens to a song, then z_3 is climbing a mountain. Can we infer the following from them? There is at least one z_3 for which if is not true that z_3 will climb a mountain if and only if z_3 will listen to a song.
 From the fact that for all z_3, z_3 will listen to a song if and only if z_3 will climb a mountain we can infer that for all z_3, if z_3 climbs a mountain, then z_3 is listening to a song. Finally, from the fact that for all z_3, if z_3 climbs a mountain, then z_3 is listening to a song, and that for all z_3, if z_3 listens to a song, then z_3 is climbing a mountain we can infer that for all z_3, z_3 will climb a mountain if and only if z_3 will listen to a song, which contradicts that There is at least one z_3 for which if is not true that z_3 will climb a mountain if and only if z_3 will listen to a song. Therefore, the answer is no.