Consider the following premises. For all x_8, if x_8 were a cashier, then x_8 is an artist. There is at least one x_8 for which if x_8 plays tennis, then x_8 is cooking. For all x_8, x_8 is a cashier if and only if x_8 will cook. 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 if x_8 plays tennis, then x_8 is an artist.
 From the fact that for all x_8, x_8 is a cashier if and only if x_8 will cook we can infer that for all x_8, if x_8 cooks, then x_8 is a cashier via universal biconditional elimination. From the fact that for all x_8, if x_8 cooks, then x_8 is a cashier, and that for all x_8, if x_8 were a cashier, then x_8 is an artist we can infer that for all x_8, if x_8 cooks, then x_8 is an artist via universal transitivity. Finally, from the fact that there is at least one x_8 for which if x_8 plays tennis, then x_8 is cooking, and that for all x_8, if x_8 cooks, then x_8 is an artist we can infer that there is at least one x_8 for which if x_8 plays tennis, then x_8 is an artist via existential transitivity. Therefore, the answer is yes.