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_5, if x_5 sleeps, then x_5 is playing a game. For all x_5, if x_5 plays a game, then x_5 is a politician. For all x_5, x_5 is happy if and only if x_5 is a politician.
For all x_5, if x_5 sleeps, then x_5 is a politician can be inferred via the universal transitivity rule. For all x_5, if x_5 were happy, then x_5 is a politician can be inferred via the universal biconditional elimination rule. For all x_5, if x_5 were a politician, then x_5 is happy can be inferred via the universal biconditional elimination rule.