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: For all x_3, x_3 will play tennis if and only if x_3 will work. There is at least one x_3 for which x_3 will not play tennis. For all x_3, x_3 will work if and only if x_3 is a doctor.
For all x_3, if x_3 plays tennis, then x_3 is working can be inferred via the universal biconditional elimination rule. For all x_3, if x_3 works, then x_3 is a doctor can be inferred via the universal biconditional elimination rule. For all x_3, if x_3 works, then x_3 is playing tennis can be inferred via the universal biconditional elimination rule. For all x_3, if x_3 were a doctor, then x_3 is working can be inferred via the universal biconditional elimination rule. There is at least one x_3 for which x_3 will not work can be inferred via the existential biconditional elimination rule.