Consider the following premises. For all x_5, x_5 is a janitor. For all x_5, if x_5 were a janitor, then x_5 is bored. For all x_5, x_5 is sad if and only if x_5 is bored. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is sad.
 From the fact that for all x_5, if x_5 were a janitor, then x_5 is bored, and that for all x_5, x_5 is a janitor we can infer that for all x_5, x_5 is bored via universal modus ponens. From the fact that for all x_5, x_5 is sad if and only if x_5 is bored we can infer that for all x_5, if x_5 were bored, then x_5 is sad via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 were bored, then x_5 is sad, and that for all x_5, x_5 is bored we can infer that for all x_5, x_5 is sad via universal modus ponens. Therefore, the answer is yes.