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_5 for which x_5 is a cashier if and only if x_5 will cook. For all x_5, if x_5 writes a letter, then x_5 is a cashier. For all x_5, x_5 will cook or x_5 will write a letter.
There is at least one x_5 for which if x_5 were a cashier, then x_5 is cooking can be inferred via the existential biconditional elimination rule. There is at least one x_5 for which if x_5 cooks, then x_5 is a cashier can be inferred via the existential biconditional elimination rule.