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, if x takes a plane, then x is a nurse. For all x, if x were poor, then x is playing a game. For all x, if x were a bartender, then x is taking a plane. There is at least one x for which if x were a nurse, then x is poor.
For all x, if x were a bartender, then x is a nurse can be inferred via the universal transitivity rule. There is at least one x for which if x were a nurse, then x is playing a game can be inferred via the existential transitivity rule. There is at least one x for which if x takes a plane, then x is poor can be inferred via the existential transitivity rule.