Consider the following premises. For all x, x will play squash if and only if x will sleep. For all x, x will sleep or x will not play squash. Can we infer the following from them? If we can, name the inference rule being used: For all x, x will sleep if and only if x will play squash.
 From the fact that for all x, x will sleep or x will not play squash we can infer that for all x, if x plays squash, then x is sleeping via universal rewriting. From the fact that for all x, x will play squash if and only if x will sleep we can infer that for all x, if x sleeps, then x is playing squash via universal biconditional elimination. Finally, from the fact that for all x, if x sleeps, then x is playing squash, and that for all x, if x plays squash, then x is sleeping we can infer that for all x, x will sleep if and only if x will play squash via universal biconditional introduction. Therefore, the answer is yes.