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 y_2 for which y_2 will play tennis if and only if y_2 is a politician. For all y_2, y_2 will not play tennis. For all y_2, y_2 is a politician if and only if y_2 will sleep. For all y_2, y_2 will climb a mountain if and only if y_2 will sleep.
For all y_2, if y_2 were a politician, then y_2 is sleeping can be inferred via the universal biconditional elimination rule. For all y_2, if y_2 climbs a mountain, then y_2 is sleeping can be inferred via the universal biconditional elimination rule. There is at least one y_2 for which if y_2 plays tennis, then y_2 is a politician can be inferred via the existential biconditional elimination rule. For all y_2, if y_2 sleeps, then y_2 is a politician can be inferred via the universal biconditional elimination rule. For all y_2, if y_2 sleeps, then y_2 is climbing a mountain can be inferred via the universal biconditional elimination rule. There is at least one y_2 for which if y_2 were a politician, then y_2 is playing tennis can be inferred via the existential biconditional elimination rule. There is at least one y_2 for which y_2 is not a politician can be inferred via the existential biconditional elimination rule.