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 William were not a doctor, then Patricia is curious. For all x_12, if x_12 cooks, then x_12 is a doctor. William is not cooking. For all x_12, if x_12 were a doctor, then x_12 is cooking.
For all x_12, x_12 will cook if and only if x_12 is a doctor can be inferred via the universal biconditional introduction rule. For all x_12, x_12 is a doctor if and only if x_12 will cook can be inferred via the universal biconditional introduction rule.