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 taking a plane if and only if Robert is cooking. For all x_10, x_10 will not take a plane. John is playing tennis if and only if Robert is cooking.
If Joseph takes a plane, then Robert is cooking can be inferred via the biconditional elimination rule. If John plays tennis, then Robert is cooking can be inferred via the biconditional elimination rule. If Robert cooks, then Joseph is taking a plane can be inferred via the biconditional elimination rule. If Robert cooks, then John is playing tennis can be inferred via the biconditional elimination rule.