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: For all x_9, x_9 is a mechanic if and only if x_9 is a politician. For all x_9, x_9 is not a politician. It is raining if and only if Thomas is a mechanic.
If it rains, then Thomas is a mechanic can be inferred via the biconditional elimination rule. If Thomas were a mechanic, then it is raining can be inferred via the biconditional elimination rule. For all x_9, if x_9 were a mechanic, then x_9 is a politician can be inferred via the universal biconditional elimination rule. For all x_9, if x_9 were a politician, then x_9 is a mechanic can be inferred via the universal biconditional elimination rule. For all x_9, x_9 is not a mechanic can be inferred via the universal biconditional elimination rule.