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: If William were rich, then Joseph is an office clerk. For all x_7, x_7 will play a game if and only if x_7 is an office clerk. Joseph is playing a game or William is rich.
For all x_7, if x_7 plays a game, then x_7 is an office clerk can be inferred via the universal biconditional elimination rule. For all x_7, if x_7 were an office clerk, then x_7 is playing a game can be inferred via the universal biconditional elimination rule.