Consider the following premises. There is at least one x for which x will play tennis if and only if x will work. For all x, if x plays tennis, then x is writing a letter. For all x, x will not write a letter. 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 not work.
 From the fact that for all x, if x plays tennis, then x is writing a letter, and that for all x, x will not write a letter we can infer that for all x, x will not play tennis via universal modus tollens. Finally, from the fact that there is at least one x for which x will play tennis if and only if x will work, and that for all x, x will not play tennis we can infer that there is at least one x for which x will not work via existential biconditional elimination. Therefore, the answer is yes.