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_9, if x_9 were a politician, then x_9 is sleeping. For all x_9, if x_9 sleeps, then x_9 is a politician. For all x_9, x_9 is excited if and only if x_9 is a politician. For all x_9, x_9 will sleep or x_9 is excited.
For all x_9, x_9 is a politician if and only if x_9 will sleep can be inferred via the universal biconditional introduction rule. For all x_9, x_9 will sleep if and only if x_9 is a politician can be inferred via the universal biconditional introduction rule. For all x_9, if x_9 were excited, then x_9 is a politician can be inferred via the universal biconditional elimination rule. For all x_9, if x_9 were a politician, then x_9 is excited can be inferred via the universal biconditional elimination rule.