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, x_7 will play tennis if and only if x_7 will play a game. For all x_7, x_7 is a poet. For all x_7, if x_7 writes a letter, then x_7 is playing a game. For all x_7, if x_7 plays tennis, then x_7 is not a poet. For all x_7, if x_7 plays a game, then x_7 is writing a letter.
For all x_7, x_7 will not play tennis can be inferred via the universal modus tollens rule. For all x_7, x_7 will write a letter if and only if x_7 will play a game can be inferred via the universal biconditional introduction rule. For all x_7, x_7 will play a game if and only if x_7 will write a letter can be inferred via the universal biconditional introduction rule. For all x_7, if x_7 plays tennis, then x_7 is playing a game can be inferred via the universal biconditional elimination rule. For all x_7, if x_7 plays a game, then x_7 is playing tennis can be inferred via the universal biconditional elimination rule.