Consider the following premises. For all z_2, if z_2 were an astronaut, then z_2 is playing squash. For all z_2, if z_2 were rich, then z_2 is an astronaut. There is at least one z_2 for which if z_2 plays squash, then z_2 is rich. Can we infer the following from them? There is at least one z_2 for which z_2 is an astronaut if and only if z_2 is rich.
 From the fact that for all z_2, if z_2 were an astronaut, then z_2 is playing squash, and that there is at least one z_2 for which if z_2 plays squash, then z_2 is rich we can infer that there is at least one z_2 for which if z_2 were an astronaut, then z_2 is rich. Finally, from the fact that there is at least one z_2 for which if z_2 were an astronaut, then z_2 is rich, and that for all z_2, if z_2 were rich, then z_2 is an astronaut we can infer that there is at least one z_2 for which z_2 is an astronaut if and only if z_2 is rich. Therefore, the answer is yes.