Consider the following premises. For all x_7, x_7 is a nurse if and only if x_7 is a politician. For all x_7, if x_7 were a janitor, then x_7 is a politician. For all x_7, x_7 is a poet. For all x_7, x_7 is a nurse or x_7 is a janitor. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is a poet and x_7 is a politician.
 From the fact that for all x_7, x_7 is a nurse if and only if x_7 is a politician we can infer that for all x_7, if x_7 were a nurse, then x_7 is a politician via universal biconditional elimination. From the fact that for all x_7, if x_7 were a nurse, then x_7 is a politician, that for all x_7, if x_7 were a janitor, then x_7 is a politician, and that for all x_7, x_7 is a nurse or x_7 is a janitor we can infer that for all x_7, x_7 is a politician via universal disjunction elimination. Finally, from the fact that for all x_7, x_7 is a poet, and that for all x_7, x_7 is a politician we can infer that for all x_7, x_7 is a poet and x_7 is a politician via universal conjunction. Therefore, the answer is yes.