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_9, if x_9 were curious, then x_9 is a lawyer. There is at least one x_9 for which x_9 is a politician if and only if x_9 is a lawyer. For all x_9, x_9 is curious or x_9 is an astronaut. For all x_9, if x_9 were an astronaut, then x_9 is a lawyer.
For all x_9, x_9 is a lawyer can be inferred via the universal disjunction elimination rule. There is at least one x_9 for which if x_9 were a politician, then x_9 is a lawyer can be inferred via the existential biconditional elimination rule. There is at least one x_9 for which if x_9 were a lawyer, then x_9 is a politician can be inferred via the existential biconditional elimination rule.