Consider the following premises. For all x, if x were sad, then x is a musician. For all x, x is a scientist. For all x, if x were sad, then x is not a scientist. For all x, if x were a musician, then x is sad. Can we infer the following from them? If we can, name the inference rule being used: For all x, x is not a musician.
 From the fact that for all x, if x were a musician, then x is sad, and that for all x, if x were sad, then x is a musician we can infer that for all x, x is a musician if and only if x is sad via universal biconditional introduction. From the fact that for all x, if x were sad, then x is not a scientist, and that for all x, x is a scientist we can infer that for all x, x is not sad via universal modus tollens. Finally, from the fact that for all x, x is a musician if and only if x is sad, and that for all x, x is not sad we can infer that for all x, x is not a musician via universal biconditional elimination. Therefore, the answer is yes.