Consider the following premises. For all z, if z were a writer, then z is playing squash. For all z, z is a writer if and only if z will play squash. For all z, if z were a musician, then z is playing squash. For all z, if z were a writer, then z is a musician. Can we infer the following from them? For all z, z is a writer if and only if z will play squash.
That is one of the premises. Therefore, the answer is yes.