Consider the following premises. For all y, if y makes tea, then y is an astronaut. For all y, y will not play a game. There is at least one y for which if y were an astronaut, then y is playing a game. For all y, if y were an astronaut, then y is making tea. Can we infer the following from them? If we can, name the inference rule being used: For all y, y will make tea.
 From the fact that for all y, if y were an astronaut, then y is making tea, and that for all y, if y makes tea, then y is an astronaut we can infer that for all y, y is an astronaut if and only if y will make tea via universal biconditional introduction. From the fact that there is at least one y for which if y were an astronaut, then y is playing a game, and that for all y, y will not play a game we can infer that there is at least one y for which y is not an astronaut via existential modus tollens. Finally, from the fact that for all y, y is an astronaut if and only if y will make tea, and that there is at least one y for which y is not an astronaut we can infer that there is at least one y for which y will not make tea via existential biconditional elimination, which contradicts that For all y, y will make tea. Therefore, the answer is no.