Consider the following premises. For all y, if y plays a game, then y is a writer. For all y, if y plays a game, then y is a writer. For all y, if y were a writer, then y is playing a game. Can we infer the following from them? If Mary plays a game, then Mary is a writer.
 From the fact that for all y, if y plays a game, then y is a writer, and that for all y, if y were a writer, then y is playing a game we can infer that for all y, y will play a game if and only if y is a writer. From the fact that for all y, y will play a game if and only if y is a writer we can infer that for all y, if y were a writer, then y is playing a game. From the fact that for all y, if y plays a game, then y is a writer, and that for all y, if y were a writer, then y is playing a game we can infer that for all y, y will play a game if and only if y is a writer. From the fact that for all y, y will play a game if and only if y is a writer we can infer that Mary is playing a game if and only if Mary is a writer. Finally, from the fact that Mary is playing a game if and only if Mary is a writer we can infer that if Mary plays a game, then Mary is a writer. Therefore, the answer is yes.