Consider the following premises. For all x, x will play tennis if and only if x is a writer. For all x, x is a writer or x is an artist. For all x, if x were an artist, then x is playing tennis. 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 play tennis.
 From the fact that for all x, x will play tennis if and only if x is a writer we can infer that for all x, if x were a writer, then x is playing tennis via universal biconditional elimination. Finally, from the fact that for all x, if x were a writer, then x is playing tennis, that for all x, if x were an artist, then x is playing tennis, and that for all x, x is a writer or x is an artist we can infer that for all x, x will play tennis via universal disjunction elimination, which contradicts that There is at least one x for which x will not play tennis. Therefore, the answer is no.