Consider the following premises. For all x_3, if x_3 were a lawyer, then x_3 is sad. For all x_3, if x_3 writes a letter, then x_3 is a lawyer. There is at least one x_3 for which if x_3 were sad, then x_3 is writing a letter. Can we infer the following from them? For all x_3, the fact that x_3 writes a letter does not imply that x_3 is sad.
That contradicts the premises. Therefore the answer is no.