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: ~r_2. q_1 -> r_2. w -> q_1. q_1 <-> w. r_2 -> q_1.
~q_1 can be inferred via the modus tollens rule. w -> r_2 can be inferred via the transitivity rule. q_1 <-> r_2 can be inferred via the biconditional introduction rule. r_2 <-> q_1 can be inferred via the biconditional introduction rule. q_1 -> w can be inferred via the biconditional elimination rule. w -> q_1 can be inferred via the biconditional elimination rule.