Consider the following premises. For all x_3, if x_3 were a writer, then x_3 is not a cashier. There is at least one x_3 for which x_3 will write a letter. For all x_3, if x_3 writes a letter, then x_3 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, if x_3 writes a letter, then x_3 is a cashier.
That is one of the premises. Therefore, the answer is yes.