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_11, x_11 is not a police officer. For all x_11, x_11 will write a letter if and only if x_11 is a nurse. For all x_11, x_11 is a police officer if and only if x_11 is a nurse. There is at least one x_11 for which x_11 is a doctor if and only if x_11 will write a letter.
For all x_11, if x_11 writes a letter, then x_11 is a nurse can be inferred via the universal biconditional elimination rule. For all x_11, if x_11 were a police officer, then x_11 is a nurse can be inferred via the universal biconditional elimination rule. There is at least one x_11 for which if x_11 were a doctor, then x_11 is writing a letter can be inferred via the existential biconditional elimination rule. For all x_11, if x_11 were a nurse, then x_11 is writing a letter can be inferred via the universal biconditional elimination rule. For all x_11, if x_11 were a nurse, then x_11 is a police officer can be inferred via the universal biconditional elimination rule. There is at least one x_11 for which if x_11 writes a letter, then x_11 is a doctor can be inferred via the existential biconditional elimination rule. For all x_11, x_11 is not a nurse can be inferred via the universal biconditional elimination rule.