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: It is not snowing. It is overcast if and only if it is snowing. If Thomas were poor, then it is overcast. If Thomas were poor, then Mary is cooking. If Mary cooks, then Thomas is poor.
If Mary cooks, then it is overcast can be inferred via the transitivity rule. Thomas is poor if and only if Mary is cooking can be inferred via the biconditional introduction rule. Mary is cooking if and only if Thomas is poor can be inferred via the biconditional introduction rule. If it is overcast, then it is snowing can be inferred via the biconditional elimination rule. If it snows, then it is overcast can be inferred via the biconditional elimination rule. It is not overcast can be inferred via the biconditional elimination rule.