Consider the following premises. Elisabeth is a writer if and only if Elisabeth is playing a game. Elisabeth is not playing a game. For all x, if x plays a game, then x is a writer. Can we infer the following from them? Elisabeth is not a writer.
 From the fact that for all x, if x plays a game, then x is a writer we can infer that if Elisabeth plays a game, then Elisabeth is a writer. From the fact that Elisabeth is a writer if and only if Elisabeth is playing a game we can infer that if Elisabeth were a writer, then Elisabeth is playing a game. From the fact that if Elisabeth plays a game, then Elisabeth is a writer, and that if Elisabeth were a writer, then Elisabeth is playing a game we can infer that Elisabeth is playing a game if and only if Elisabeth is a writer. Finally, from the fact that Elisabeth is playing a game if and only if Elisabeth is a writer, and that Elisabeth is not playing a game we can infer that Elisabeth is not a writer. Therefore, the answer is yes.