Consider the following premises. For all x_7, x_7 is excited if and only if x_7 will sleep. For all x_7, x_7 will take a plane or x_7 is excited. For all x_7, if x_7 takes a plane, then x_7 is sleeping. For all x_7, x_7 will work. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will work and x_7 will sleep.
 From the fact that for all x_7, x_7 is excited if and only if x_7 will sleep we can infer that for all x_7, if x_7 were excited, then x_7 is sleeping via universal biconditional elimination. From the fact that for all x_7, if x_7 takes a plane, then x_7 is sleeping, that for all x_7, if x_7 were excited, then x_7 is sleeping, and that for all x_7, x_7 will take a plane or x_7 is excited we can infer that for all x_7, x_7 will sleep via universal disjunction elimination. Finally, from the fact that for all x_7, x_7 will work, and that for all x_7, x_7 will sleep we can infer that for all x_7, x_7 will work and x_7 will sleep via universal conjunction. Therefore, the answer is yes.