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: James is poor if and only if Patricia is running. For all x, if x listens to a song, then x is poor. For all x, x will not listen to a song. For all x, if x were poor, then x is listening to a song.
If James were poor, then Patricia is running can be inferred via the biconditional elimination rule. If Patricia goes running, then James is poor can be inferred via the biconditional elimination rule. For all x, x is not poor can be inferred via the universal modus tollens rule. For all x, x will listen to a song if and only if x is poor can be inferred via the universal biconditional introduction rule. For all x, x is poor if and only if x will listen to a song can be inferred via the universal biconditional introduction rule.