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: If Elisabeth were rich, then William is a nurse. It is not snowing. If it is late, then Elisabeth is rich. It is overcast if and only if Michael is sleeping. If Michael sleeps, then it is late. It is snowing if and only if William is a nurse.
If it is late, then William is a nurse can be inferred via the transitivity rule. If Michael sleeps, then Elisabeth is rich can be inferred via the transitivity rule. If it is overcast, then Michael is sleeping can be inferred via the biconditional elimination rule. If it snows, then William is a nurse can be inferred via the biconditional elimination rule. If Michael sleeps, then it is overcast can be inferred via the biconditional elimination rule. If William were a nurse, then it is snowing can be inferred via the biconditional elimination rule. William is not a nurse can be inferred via the biconditional elimination rule.