Consider the following premises. There is at least one x_8 for which if x_8 writes a letter, then x_8 is working. For all x_8, x_8 is not a musician. For all x_8, x_8 will work if and only if x_8 is a musician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 will not write a letter.
 From the fact that for all x_8, x_8 will work if and only if x_8 is a musician we can infer that for all x_8, if x_8 works, then x_8 is a musician via universal biconditional elimination. From the fact that there is at least one x_8 for which if x_8 writes a letter, then x_8 is working, and that for all x_8, if x_8 works, then x_8 is a musician we can infer that there is at least one x_8 for which if x_8 writes a letter, then x_8 is a musician via existential transitivity. Finally, from the fact that there is at least one x_8 for which if x_8 writes a letter, then x_8 is a musician, and that for all x_8, x_8 is not a musician we can infer that there is at least one x_8 for which x_8 will not write a letter via existential modus tollens. Therefore, the answer is yes.