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: If it rains, then Barbara is writing a letter. Mary is drinking water if and only if it is raining. Mary is drinking water if and only if it is overcast. If it is overcast, then Mary is drinking water. Barbara is not writing a letter.
It is not raining can be inferred via the modus tollens rule. If Mary drinks water, then it is raining can be inferred via the biconditional elimination rule. If Mary drinks water, then it is overcast can be inferred via the biconditional elimination rule. If it rains, then Mary is drinking water can be inferred via the biconditional elimination rule. If it is overcast, then Mary is drinking water can be inferred via the biconditional elimination rule.