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, x will play tennis if and only if x is poor. For all x, x is poor or x will drink water. For all x, if x sleeps, then x is playing tennis. For all x, if x were poor, then x is sleeping. There is at least one x for which if x drinks water, then x is playing tennis.
For all x, if x were poor, then x is playing tennis can be inferred via the universal transitivity rule. For all x, if x plays tennis, then x is poor can be inferred via the universal biconditional elimination rule. For all x, if x were poor, then x is playing tennis can be inferred via the universal biconditional elimination rule.