Consider the following premises. For all x_3, x_3 will work or x_3 is not an artist. For all x_3, if x_3 works, then x_3 is an artist. For all x_3, x_3 is not an artist. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, x_3 will not work.
 From the fact that for all x_3, x_3 will work or x_3 is not an artist we can infer that for all x_3, if x_3 were an artist, then x_3 is working via universal rewriting. From the fact that for all x_3, if x_3 works, then x_3 is an artist, and that for all x_3, if x_3 were an artist, then x_3 is working we can infer that for all x_3, x_3 will work if and only if x_3 is an artist via universal biconditional introduction. Finally, from the fact that for all x_3, x_3 will work if and only if x_3 is an artist, and that for all x_3, x_3 is not an artist we can infer that for all x_3, x_3 will not work via universal biconditional elimination. Therefore, the answer is yes.