Consider the following premises. If Barbara plays squash, then Mary is writing a letter. Barbara is playing squash or Mary is sleeping. For all y, y will write a letter if and only if y will sleep. Can we infer the following from them? If we can, name the inference rule being used: Mary is writing a letter.
 From the fact that for all y, y will write a letter if and only if y will sleep we can infer that Mary is writing a letter if and only if Mary is sleeping via universal instantiation. From the fact that Mary is writing a letter if and only if Mary is sleeping we can infer that if Mary sleeps, then Mary is writing a letter via biconditional elimination. Finally, from the fact that if Barbara plays squash, then Mary is writing a letter, that if Mary sleeps, then Mary is writing a letter, and that Barbara is playing squash or Mary is sleeping we can infer that Mary is writing a letter via disjunction elimination. Therefore, the answer is yes.