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_2, x_2 is an office clerk if and only if x_2 will play tennis. For all x_2, x_2 is an office clerk if and only if x_2 is happy. For all x_2, if x_2 were happy, then x_2 is listening to a song.
For all x_2, if x_2 were an office clerk, then x_2 is playing tennis can be inferred via the universal biconditional elimination rule. For all x_2, if x_2 were an office clerk, then x_2 is happy can be inferred via the universal biconditional elimination rule. For all x_2, if x_2 plays tennis, then x_2 is an office clerk can be inferred via the universal biconditional elimination rule. For all x_2, if x_2 were happy, then x_2 is an office clerk can be inferred via the universal biconditional elimination rule.