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: It is not cloudy. If Susan doesn't write a letter, then Mary is cooking. It is cloudy if and only if Susan is writing a letter. If Mary cooks, then Jennifer is climbing a mountain.
If Susan doesn't write a letter, then Jennifer is climbing a mountain can be inferred via the transitivity rule. If it is cloudy, then Susan is writing a letter can be inferred via the biconditional elimination rule. If Susan writes a letter, then it is cloudy can be inferred via the biconditional elimination rule. Susan is not writing a letter can be inferred via the biconditional elimination rule.