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 were rich, then x_5 is playing a game. For all x_5, if x_5 were excited, then x_5 is playing a game. For all x_5, if x_5 plays a game, then x_5 is excited.
For all x_5, if x_5 were rich, then x_5 is excited can be inferred via the universal transitivity rule. For all x_5, x_5 is excited if and only if x_5 will play a game can be inferred via the universal biconditional introduction rule. For all x_5, x_5 will play a game if and only if x_5 is excited can be inferred via the universal biconditional introduction rule.