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: Robert is a doctor if and only if William is a poet. It is windy if and only if Robert is a doctor. Thomas is climbing a mountain. It is not windy.
Thomas is climbing a mountain and it is not windy can be inferred via the conjunction rule. It is not windy and Thomas is climbing a mountain can be inferred via the conjunction rule. If Robert were a doctor, then William is a poet can be inferred via the biconditional elimination rule. If it is windy, then Robert is a doctor can be inferred via the biconditional elimination rule. If William were a poet, then Robert is a doctor can be inferred via the biconditional elimination rule. If Robert were a doctor, then it is windy can be inferred via the biconditional elimination rule. Robert is not a doctor can be inferred via the biconditional elimination rule.