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 Patricia were sad, then Barbara is cooking. For all x, x will cook if and only if x is a police officer. If Barbara were a police officer, then Patricia is sad.
If Barbara were a police officer, then Barbara is cooking can be inferred via the transitivity rule. For all x, if x cooks, then x is a police officer can be inferred via the universal biconditional elimination rule. For all x, if x were a police officer, then x is cooking can be inferred via the universal biconditional elimination rule.