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: David is happy or Michael is a nurse. If Michael were a nurse, then it is raining. If it rains, then David is happy. It is raining if and only if David is happy.
If Michael were a nurse, then David is happy can be inferred via the transitivity rule. If it rains, then David is happy can be inferred via the biconditional elimination rule. If David were happy, then it is raining can be inferred via the biconditional elimination rule.