Consider the following premises. For all x_7, x_7 is an artist or x_7 is not a cashier. There is at least one x_7 for which if x_7 were an artist, then x_7 is excited. For all x_7, if x_7 were excited, then x_7 is a cashier. For all x_7, x_7 is not an artist. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is a cashier.
 From the fact that there is at least one x_7 for which if x_7 were an artist, then x_7 is excited, and that for all x_7, if x_7 were excited, then x_7 is a cashier we can infer that there is at least one x_7 for which if x_7 were an artist, then x_7 is a cashier via existential transitivity. From the fact that for all x_7, x_7 is an artist or x_7 is not a cashier we can infer that for all x_7, if x_7 were a cashier, then x_7 is an artist via universal rewriting. From the fact that there is at least one x_7 for which if x_7 were an artist, then x_7 is a cashier, and that for all x_7, if x_7 were a cashier, then x_7 is an artist we can infer that there is at least one x_7 for which x_7 is an artist if and only if x_7 is a cashier via existential biconditional introduction. Finally, from the fact that there is at least one x_7 for which x_7 is an artist if and only if x_7 is a cashier, and that for all x_7, x_7 is not an artist we can infer that there is at least one x_7 for which x_7 is not a cashier via existential biconditional elimination, which contradicts that For all x_7, x_7 is a cashier. Therefore, the answer is no.