Consider the following premises. If it snows, then it is windy. For all y, y will not play a game. If it is windy, then it is snowing. Joseph is playing a game if and only if it is windy. Can we infer the following from them? It is not snowing.
 From the fact that if it snows, then it is windy, and that if it is windy, then it is snowing we can infer that it is snowing if and only if it is windy. From the fact that for all y, y will not play a game we can infer that Joseph is not playing a game. From the fact that Joseph is playing a game if and only if it is windy, and that Joseph is not playing a game we can infer that it is not windy. Finally, from the fact that it is snowing if and only if it is windy, and that it is not windy we can infer that it is not snowing. Therefore, the answer is yes.