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: There is at least one x_7 for which if x_7 works, then x_7 is rich. For all x_7, if x_7 were rich, then x_7 is working. For all x_7, x_7 will work.
There is at least one x_7 for which x_7 is rich can be inferred via the existential modus ponens rule. There is at least one x_7 for which x_7 will work if and only if x_7 is rich can be inferred via the existential biconditional introduction rule. There is at least one x_7 for which x_7 is rich if and only if x_7 will work can be inferred via the existential biconditional introduction rule.