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 John writes a letter, then it is cloudy. If John writes a letter, then Richard is a soldier. If it is cloudy, then John is writing a letter.
If it is cloudy, then Richard is a soldier can be inferred via the transitivity rule. John is writing a letter if and only if it is cloudy can be inferred via the biconditional introduction rule. It is cloudy if and only if John is writing a letter can be inferred via the biconditional introduction rule.