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_15, x_15 is rich if and only if x_15 is a soldier. There is at least one x_15 for which if x_15 were an electrician, then x_15 is sad. For all x_15, if x_15 were sad, then x_15 is a soldier. For all x_15, if x_15 were rich, then x_15 is an electrician.
There is at least one x_15 for which if x_15 were an electrician, then x_15 is a soldier can be inferred via the existential transitivity rule. There is at least one x_15 for which if x_15 were rich, then x_15 is sad can be inferred via the existential transitivity rule. For all x_15, if x_15 were rich, then x_15 is a soldier can be inferred via the universal biconditional elimination rule. For all x_15, if x_15 were a soldier, then x_15 is rich can be inferred via the universal biconditional elimination rule.