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 x_7, if x_7 plays a game, then x_7 is working. For all x_7, if x_7 works, then x_7 is playing a game. For all x_7, if x_7 works, then x_7 is playing tennis. There is at least one x_7 for which if x_7 plays tennis, then x_7 is working. For all x_7, x_7 will not play a game.
For all x_7, x_7 will not work can be inferred via the universal modus tollens rule. For all x_7, if x_7 plays a game, then x_7 is playing tennis can be inferred via the universal transitivity rule. There is at least one x_7 for which if x_7 plays tennis, then x_7 is playing a game can be inferred via the existential transitivity rule. For all x_7, x_7 will play a game if and only if x_7 will work can be inferred via the universal biconditional introduction rule. For all x_7, x_7 will work if and only if x_7 will play a game can be inferred via the universal biconditional introduction rule. There is at least one x_7 for which x_7 will play tennis if and only if x_7 will work can be inferred via the existential biconditional introduction rule. There is at least one x_7 for which x_7 will work if and only if x_7 will play tennis can be inferred via the existential biconditional introduction rule.