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 z_1, z_1 will play a game if and only if z_1 is an office clerk. For all z_1, if z_1 were an office clerk, then z_1 is playing a game. There is at least one z_1 for which if z_1 were an office clerk, then z_1 is playing a game.
For all z_1, if z_1 plays a game, then z_1 is an office clerk can be inferred via the universal biconditional elimination rule. For all z_1, if z_1 were an office clerk, then z_1 is playing a game can be inferred via the universal biconditional elimination rule.