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_15, x_15 is rich. For all x_15, x_15 will play tennis or x_15 is not happy. There is at least one x_15 for which x_15 is an astronaut if and only if x_15 will play tennis. For all x_15, if x_15 were rich, then x_15 is happy.
For all x_15, x_15 is happy can be inferred via the universal modus ponens rule. For all x_15, if x_15 were happy, then x_15 is playing tennis can be inferred via the universal rewriting rule. There is at least one x_15 for which if x_15 were an astronaut, then x_15 is playing tennis can be inferred via the existential biconditional elimination rule. There is at least one x_15 for which if x_15 plays tennis, then x_15 is an astronaut can be inferred via the existential biconditional elimination rule.