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 rich. For all x_5, if x_5 were rich, then x_5 is cooking. For all x_5, x_5 is a politician. For all x_5, if x_5 climbs a mountain, then x_5 is cooking.
For all x_5, x_5 will cook can be inferred via the universal modus ponens rule. For all x_5, x_5 is rich and x_5 is a politician can be inferred via the universal conjunction rule. For all x_5, x_5 is a politician and x_5 is rich can be inferred via the universal conjunction rule.