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, x is not excited. For all x, x will play a game if and only if x is excited. Mary is a writer if and only if Robert is playing a game.
If Mary were a writer, then Robert is playing a game can be inferred via the biconditional elimination rule. If Robert plays a game, then Mary is a writer can be inferred via the biconditional elimination rule. For all x, if x plays a game, then x is excited can be inferred via the universal biconditional elimination rule. For all x, if x were excited, then x is playing a game can be inferred via the universal biconditional elimination rule. For all x, x will not play a game can be inferred via the universal biconditional elimination rule.