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_8, x_8 is a doctor if and only if x_8 will play a game. For all x_8, x_8 will not play a game. For all x_8, if x_8 plays a game, then x_8 is a doctor. For all x_8, x_8 is an electrician if and only if x_8 is a doctor.
For all x_8, if x_8 were a doctor, then x_8 is playing a game can be inferred via the universal biconditional elimination rule. For all x_8, if x_8 were an electrician, then x_8 is a doctor can be inferred via the universal biconditional elimination rule. For all x_8, if x_8 plays a game, then x_8 is a doctor can be inferred via the universal biconditional elimination rule. For all x_8, if x_8 were a doctor, then x_8 is an electrician can be inferred via the universal biconditional elimination rule. For all x_8, x_8 is not a doctor can be inferred via the universal biconditional elimination rule.