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_10, x_10 will not play tennis. For all x_10, if x_10 cooks, then x_10 is playing tennis. For all x_10, x_10 will play tennis if and only if x_10 will cook. For all x_10, if x_10 plays tennis, then x_10 is cooking.
For all x_10, x_10 will not cook can be inferred via the universal modus tollens rule. For all x_10, x_10 will cook if and only if x_10 will play tennis can be inferred via the universal biconditional introduction rule. For all x_10, x_10 will play tennis if and only if x_10 will cook can be inferred via the universal biconditional introduction rule. For all x_10, if x_10 plays tennis, then x_10 is cooking can be inferred via the universal biconditional elimination rule. For all x_10, if x_10 cooks, then x_10 is playing tennis can be inferred via the universal biconditional elimination rule. For all x_10, x_10 will not cook can be inferred via the universal biconditional elimination rule.