Consider the following premises. For all z_4, if z_4 were an electrician, then z_4 is a musician. There is at least one z_4 for which if z_4 were an astronaut, then z_4 is writing a letter. For all z_4, z_4 is an electrician if and only if z_4 will write a letter. Can we infer the following from them? For all z_4, the fact that z_4 were an astronaut does not imply that z_4 is a musician.
That contradicts the premises. Therefore the answer is no.