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 z, if z writes a letter, then z is an astronaut. There is at least one z for which if z were an astronaut, then z is writing a letter. For all z, z is a cashier if and only if z will write a letter.
There is at least one z for which z is an astronaut if and only if z will write a letter can be inferred via the existential biconditional introduction rule. There is at least one z for which z will write a letter if and only if z is an astronaut can be inferred via the existential biconditional introduction rule. For all z, if z were a cashier, then z is writing a letter can be inferred via the universal biconditional elimination rule. For all z, if z writes a letter, then z is a cashier can be inferred via the universal biconditional elimination rule.