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 Joseph were a doctor, then William is poor. If it is sunny, then John is taking a plane. If it is sunny, then Joseph is a doctor. If John takes a plane, then it is sunny.
If it is sunny, then William is poor can be inferred via the transitivity rule. If John takes a plane, then Joseph is a doctor can be inferred via the transitivity rule. It is sunny if and only if John is taking a plane can be inferred via the biconditional introduction rule. John is taking a plane if and only if it is sunny can be inferred via the biconditional introduction rule.