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, z is bored if and only if z is a bartender. There is at least one z for which z is bored if and only if z is a nurse. For all z, z is not a bartender.
For all z, if z were bored, then z is a bartender can be inferred via the universal biconditional elimination rule. There is at least one z for which if z were bored, then z is a nurse can be inferred via the existential biconditional elimination rule. For all z, if z were a bartender, then z is bored can be inferred via the universal biconditional elimination rule. There is at least one z for which if z were a nurse, then z is bored can be inferred via the existential biconditional elimination rule. For all z, z is not bored can be inferred via the universal biconditional elimination rule.