Consider the following premises. There is at least one x for which x is a writer if and only if x will play squash. For all x, if x were a cashier, then x is playing squash. For all x, x is a writer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x will play squash.
 From the fact that for all x, x is a writer we can infer that for all x, x is a writer or x is a cashier via universal addition. From the fact that there is at least one x for which x is a writer if and only if x will play squash we can infer that there is at least one x for which if x were a writer, then x is playing squash via existential biconditional elimination. Finally, from the fact that there is at least one x for which if x were a writer, then x is playing squash, that for all x, if x were a cashier, then x is playing squash, and that for all x, x is a writer or x is a cashier we can infer that there is at least one x for which x will play squash via existential disjunction elimination. Therefore, the answer is yes.