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: There is at least one x_2 for which if x_2 were a soldier, then x_2 is writing a letter. For all x_2, if x_2 were a bartender, then x_2 is a lawyer. For all x_2, if x_2 were a lawyer, then x_2 is a soldier.
For all x_2, if x_2 were a bartender, then x_2 is a soldier can be inferred via the universal transitivity rule. There is at least one x_2 for which if x_2 were a lawyer, then x_2 is writing a letter can be inferred via the existential transitivity rule.