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_2, if y_2 cooks, then y_2 is poor. For all y_2, y_2 will play a game or y_2 will cook. For all y_2, y_2 is a writer. For all y_2, y_2 will play a game if and only if y_2 is sad. For all y_2, y_2 is not sad.
For all y_2, if y_2 plays a game, then y_2 is sad can be inferred via the universal biconditional elimination rule. For all y_2, if y_2 were sad, then y_2 is playing a game can be inferred via the universal biconditional elimination rule. For all y_2, y_2 will not play a game can be inferred via the universal biconditional elimination rule.