Consider the following premises. For all x_4, if x_4 cooks, then x_4 is happy. There is at least one x_4 for which x_4 is an artist or x_4 will cook. For all x_4, x_4 is happy if and only if x_4 is an artist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 is happy.
 From the fact that for all x_4, x_4 is happy if and only if x_4 is an artist we can infer that for all x_4, if x_4 were an artist, then x_4 is happy via universal biconditional elimination. Finally, from the fact that for all x_4, if x_4 were an artist, then x_4 is happy, that for all x_4, if x_4 cooks, then x_4 is happy, and that there is at least one x_4 for which x_4 is an artist or x_4 will cook we can infer that there is at least one x_4 for which x_4 is happy via existential disjunction elimination. Therefore, the answer is yes.