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: Sarah is not rich. Sarah is poor if and only if Joseph is climbing a mountain. For all y, y is poor if and only if y is rich. Joseph is climbing a mountain if and only if Thomas is listening to a song.
If Sarah were poor, then Joseph is climbing a mountain can be inferred via the biconditional elimination rule. If Joseph climbs a mountain, then Thomas is listening to a song can be inferred via the biconditional elimination rule. If Joseph climbs a mountain, then Sarah is poor can be inferred via the biconditional elimination rule. If Thomas listens to a song, then Joseph is climbing a mountain can be inferred via the biconditional elimination rule. For all y, if y were poor, then y is rich can be inferred via the universal biconditional elimination rule. For all y, if y were rich, then y is poor can be inferred via the universal biconditional elimination rule.