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_10, if x_10 were a police officer, then x_10 is a doctor. For all x_10, if x_10 cooks, then x_10 is a doctor. There is at least one x_10 for which if x_10 were a doctor, then x_10 is cooking. For all x_10, if x_10 cooks, then x_10 is a police officer.
For all x_10, if x_10 cooks, then x_10 is a doctor can be inferred via the universal transitivity rule. There is at least one x_10 for which if x_10 were a doctor, then x_10 is a police officer can be inferred via the existential transitivity rule. There is at least one x_10 for which if x_10 were a police officer, then x_10 is cooking can be inferred via the existential transitivity rule. There is at least one x_10 for which x_10 is a doctor if and only if x_10 will cook can be inferred via the existential biconditional introduction rule. There is at least one x_10 for which x_10 will cook if and only if x_10 is a doctor can be inferred via the existential biconditional introduction rule.