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_9 for which x_9 will work if and only if x_9 is an office clerk. For all x_9, if x_9 writes a letter, then x_9 is working. For all x_9, if x_9 were a cashier, then x_9 is an office clerk. For all x_9, x_9 will write a letter or x_9 is a cashier.
There is at least one x_9 for which if x_9 works, then x_9 is an office clerk can be inferred via the existential biconditional elimination rule. There is at least one x_9 for which if x_9 were an office clerk, then x_9 is working can be inferred via the existential biconditional elimination rule.