Consider the following premises. For all x_12, x_12 is not an artist. There is at least one x_12 for which x_12 is sad if and only if x_12 is an artist. For all x_12, x_12 will make tea if and only if x_12 is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 will not make tea.
 From the fact that there is at least one x_12 for which x_12 is sad if and only if x_12 is an artist we can infer that there is at least one x_12 for which if x_12 were sad, then x_12 is an artist via existential biconditional elimination. From the fact that there is at least one x_12 for which if x_12 were sad, then x_12 is an artist, and that for all x_12, x_12 is not an artist we can infer that there is at least one x_12 for which x_12 is not sad via existential modus tollens. Finally, from the fact that for all x_12, x_12 will make tea if and only if x_12 is sad, and that there is at least one x_12 for which x_12 is not sad we can infer that there is at least one x_12 for which x_12 will not make tea via existential biconditional elimination. Therefore, the answer is yes.