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: Elisabeth is writing a letter if and only if it is cloudy. Patricia is not an electrician. It is cloudy if and only if Patricia is bored. For all x_12, x_12 is an electrician if and only if x_12 is bored.
If Elisabeth writes a letter, then it is cloudy can be inferred via the biconditional elimination rule. If it is cloudy, then Patricia is bored can be inferred via the biconditional elimination rule. If it is cloudy, then Elisabeth is writing a letter can be inferred via the biconditional elimination rule. If Patricia were bored, then it is cloudy can be inferred via the biconditional elimination rule. For all x_12, if x_12 were an electrician, then x_12 is bored can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 were bored, then x_12 is an electrician can be inferred via the universal biconditional elimination rule.