Consider the following premises. For all x_7, x_7 is an office clerk or x_7 is a janitor. There is at least one x_7 for which x_7 is an office clerk if and only if x_7 is happy. For all x_7, x_7 is not happy. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is not a janitor.
 From the fact that there is at least one x_7 for which x_7 is an office clerk if and only if x_7 is happy, and that for all x_7, x_7 is not happy we can infer that there is at least one x_7 for which x_7 is not an office clerk via existential biconditional elimination. Finally, from the fact that for all x_7, x_7 is an office clerk or x_7 is a janitor, and that there is at least one x_7 for which x_7 is not an office clerk we can infer that there is at least one x_7 for which x_7 is a janitor via existential disjunctive syllogism, which contradicts that For all x_7, x_7 is not a janitor. Therefore, the answer is no.