Consider the following premises. For all x_17, x_17 will cook. For all x_17, if x_17 were a lawyer, then x_17 is sad. For all x_17, if x_17 were a police officer, then x_17 is a lawyer. For all x_17, x_17 is sad if and only if x_17 is an artist. There is at least one x_17 for which x_17 is a police officer or x_17 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_17 for which x_17 will cook and x_17 is sad.
 From the fact that for all x_17, x_17 is sad if and only if x_17 is an artist we can infer that for all x_17, if x_17 were an artist, then x_17 is sad via universal biconditional elimination. From the fact that for all x_17, if x_17 were a police officer, then x_17 is a lawyer, and that for all x_17, if x_17 were a lawyer, then x_17 is sad we can infer that for all x_17, if x_17 were a police officer, then x_17 is sad via universal transitivity. From the fact that for all x_17, if x_17 were a police officer, then x_17 is sad, that for all x_17, if x_17 were an artist, then x_17 is sad, and that there is at least one x_17 for which x_17 is a police officer or x_17 is an artist we can infer that there is at least one x_17 for which x_17 is sad via existential disjunction elimination. Finally, from the fact that for all x_17, x_17 will cook, and that there is at least one x_17 for which x_17 is sad we can infer that there is at least one x_17 for which x_17 will cook and x_17 is sad via existential conjunction. Therefore, the answer is yes.