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, if x plays a game, then x is reading a book. For all x, x is an electrician or x will play a game. For all x, x is an electrician if and only if x will read a book. For all x, if x reads a book, then x is playing a game.
For all x, x will play a game if and only if x will read a book can be inferred via the universal biconditional introduction rule. For all x, x will read a book if and only if x will play a game can be inferred via the universal biconditional introduction rule. For all x, if x were an electrician, then x is reading a book can be inferred via the universal biconditional elimination rule. For all x, if x reads a book, then x is an electrician can be inferred via the universal biconditional elimination rule.