Consider the following premises. For all y_1, if y_1 were a lawyer, then y_1 is a poet. For all y_1, y_1 is a soldier if and only if y_1 is a lawyer. For all y_1, if y_1 were a poet, then y_1 is playing a game. Can we infer the following from them? There is at least one y_1 for which the fact that y_1 were a soldier does not imply that y_1 is playing a game.
 From the fact that for all y_1, y_1 is a soldier if and only if y_1 is a lawyer we can infer that for all y_1, if y_1 were a soldier, then y_1 is a lawyer. From the fact that for all y_1, if y_1 were a lawyer, then y_1 is a poet, and that for all y_1, if y_1 were a poet, then y_1 is playing a game we can infer that for all y_1, if y_1 were a lawyer, then y_1 is playing a game. Finally, from the fact that for all y_1, if y_1 were a soldier, then y_1 is a lawyer, and that for all y_1, if y_1 were a lawyer, then y_1 is playing a game we can infer that for all y_1, if y_1 were a soldier, then y_1 is playing a game, which contradicts that There is at least one y_1 for which the fact that y_1 were a soldier does not imply that y_1 is playing a game. Therefore, the answer is no.