Consider the following premises. For all x, x will make tea. For all x, if x plays tennis, then x is a writer. There is at least one x for which x will play tennis if and only if x will make tea. Can we infer the following from them? If we can, name the inference rule being used: For all x, x is not a writer.
 From the fact that there is at least one x for which x will play tennis if and only if x will make tea we can infer that there is at least one x for which if x makes tea, then x is playing tennis via existential biconditional elimination. From the fact that there is at least one x for which if x makes tea, then x is playing tennis, and that for all x, x will make tea we can infer that there is at least one x for which x will play tennis via existential modus ponens. Finally, from the fact that for all x, if x plays tennis, then x is a writer, and that there is at least one x for which x will play tennis we can infer that there is at least one x for which x is a writer via existential modus ponens, which contradicts that For all x, x is not a writer. Therefore, the answer is no.