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 z, z will listen to a song if and only if z is a police officer. For all z, z is a cashier if and only if z is a police officer. For all z, z will drink water if and only if z will listen to a song. For all z, z will not drink water.
For all z, if z listens to a song, then z is a police officer can be inferred via the universal biconditional elimination rule. For all z, if z were a cashier, then z is a police officer can be inferred via the universal biconditional elimination rule. For all z, if z drinks water, then z is listening to a song can be inferred via the universal biconditional elimination rule. For all z, if z were a police officer, then z is listening to a song can be inferred via the universal biconditional elimination rule. For all z, if z were a police officer, then z is a cashier can be inferred via the universal biconditional elimination rule. For all z, if z listens to a song, then z is drinking water can be inferred via the universal biconditional elimination rule. For all z, z will not listen to a song can be inferred via the universal biconditional elimination rule.