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_7, if x_7 were happy, then x_7 is a police officer. For all x_7, if x_7 were a police officer, then x_7 is curious. For all x_7, if x_7 were a police officer, then x_7 is happy. There is at least one x_7 for which if x_7 were curious, then x_7 is happy.
For all x_7, if x_7 were happy, then x_7 is curious can be inferred via the universal transitivity rule. There is at least one x_7 for which if x_7 were curious, then x_7 is a police officer can be inferred via the existential transitivity rule. There is at least one x_7 for which if x_7 were a police officer, then x_7 is happy can be inferred via the existential transitivity rule. For all x_7, x_7 is happy if and only if x_7 is a police officer can be inferred via the universal biconditional introduction rule. For all x_7, x_7 is a police officer if and only if x_7 is happy can be inferred via the universal biconditional introduction rule.