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 Joseph were a scientist, then Patricia is climbing a mountain. It is snowing if and only if Mary is rich. Mary is rich or Joseph is a scientist. If Patricia climbs a mountain, then it is snowing.
If Joseph were a scientist, then it is snowing can be inferred via the transitivity rule. If it snows, then Mary is rich can be inferred via the biconditional elimination rule. If Mary were rich, then it is snowing can be inferred via the biconditional elimination rule.