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: Barbara is a carpenter. It is cloudy if and only if James is poor. If James were poor, then Patricia is curious. If Barbara were a carpenter, then it is cloudy.
It is cloudy can be inferred via the modus ponens rule. If it is cloudy, then James is poor can be inferred via the biconditional elimination rule. If James were poor, then it is cloudy can be inferred via the biconditional elimination rule.