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, x_5 is a nurse. For all x_5, if x_5 were a nurse, then x_5 is an astronaut. For all x_5, if x_5 were an astronaut, then x_5 is playing a game. For all x_5, x_5 will climb a mountain.
For all x_5, x_5 is an astronaut can be inferred via the universal modus ponens rule. For all x_5, if x_5 were a nurse, then x_5 is playing a game can be inferred via the universal transitivity rule. For all x_5, x_5 is a nurse and x_5 will climb a mountain can be inferred via the universal conjunction rule. For all x_5, x_5 will climb a mountain and x_5 is a nurse can be inferred via the universal conjunction rule.