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: Joseph is a doctor if and only if Michael is a lawyer. Michael is cooking or Joseph is a doctor. For all x_10, if x_10 cooks, then x_10 is a lawyer.
If Joseph were a doctor, then Michael is a lawyer can be inferred via the biconditional elimination rule. If Michael were a lawyer, then Joseph is a doctor can be inferred via the biconditional elimination rule.