Consider the following premises. There is at least one z_4 for which if z_4 plays squash, then z_4 is a carpenter. For all z_4, z_4 is a carpenter if and only if z_4 will play squash. Can we infer the following from them? There is at least one z_4 for which z_4 is a carpenter if and only if z_4 will play squash.
 From the fact that for all z_4, z_4 is a carpenter if and only if z_4 will play squash we can infer that for all z_4, if z_4 were a carpenter, then z_4 is playing squash. Finally, from the fact that for all z_4, if z_4 were a carpenter, then z_4 is playing squash, and that there is at least one z_4 for which if z_4 plays squash, then z_4 is a carpenter we can infer that there is at least one z_4 for which z_4 is a carpenter if and only if z_4 will play squash. Therefore, the answer is yes.