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