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: There is at least one z_1 for which z_1 is rich if and only if z_1 will play tennis. For all z_1, z_1 is rich if and only if z_1 is a soldier. For all z_1, if z_1 were a soldier, then z_1 is playing a game. For all z_1, z_1 will not play a game.
For all z_1, z_1 is not a soldier can be inferred via the universal modus tollens rule. For all z_1, if z_1 were rich, then z_1 is a soldier can be inferred via the universal biconditional elimination rule. There is at least one z_1 for which if z_1 were rich, then z_1 is playing tennis can be inferred via the existential biconditional elimination rule. For all z_1, if z_1 were a soldier, then z_1 is rich can be inferred via the universal biconditional elimination rule. There is at least one z_1 for which if z_1 plays tennis, then z_1 is rich can be inferred via the existential biconditional elimination rule.