What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: For all y, y is an astronaut if and only if y will play a game. There is at least one y for which if y were a politician, then y is not playing a game. For all y, y is an astronaut or y will listen to a song. For all y, if y listens to a song, then y is playing a game.
For all y, if y were an astronaut, then y is playing a game can be inferred via the universal biconditional elimination rule. For all y, if y plays a game, then y is an astronaut can be inferred via the universal biconditional elimination rule.