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: Michael is playing a game if and only if it is cloudy. It is not cloudy. For all x_12, x_12 is a bartender if and only if x_12 will play a game.
If Michael plays a game, then it is cloudy can be inferred via the biconditional elimination rule. If it is cloudy, then Michael is playing a game can be inferred via the biconditional elimination rule. Michael is not playing a game can be inferred via the biconditional elimination rule. For all x_12, if x_12 were a bartender, then x_12 is playing a game can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 plays a game, then x_12 is a bartender can be inferred via the universal biconditional elimination rule.