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, if y sleeps, then y is a scientist. For all y, y will sleep if and only if y will play a game. For all y, y will sleep if and only if y is a scientist.
For all y, if y sleeps, then y is playing a game can be inferred via the universal biconditional elimination rule. For all y, if y sleeps, then y is a scientist can be inferred via the universal biconditional elimination rule. For all y, if y plays a game, then y is sleeping can be inferred via the universal biconditional elimination rule. For all y, if y were a scientist, then y is sleeping can be inferred via the universal biconditional elimination rule.