Consider the following premises. For all y, y is a lawyer. For all y, if y were a lawyer, then y is bored. For all y, y will play a game. For all y, if y were an astronaut, then y is bored. Can we infer the following from them? If we can, name the inference rule being used: For all y, y is bored and y will play a game.
 From the fact that for all y, y is a lawyer we can infer that for all y, y is a lawyer or y is an astronaut via universal addition. From the fact that for all y, if y were a lawyer, then y is bored, that for all y, if y were an astronaut, then y is bored, and that for all y, y is a lawyer or y is an astronaut we can infer that for all y, y is bored via universal disjunction elimination. Finally, from the fact that for all y, y is bored, and that for all y, y will play a game we can infer that for all y, y is bored and y will play a game via universal conjunction. Therefore, the answer is yes.