Consider the following premises. Robert is a soldier if and only if Elisabeth is a scientist. Elisabeth is a scientist or Robert is not a soldier. For all y_1, y_1 is not a soldier. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not a scientist.
 From the fact that for all y_1, y_1 is not a soldier we can infer that Robert is not a soldier via universal instantiation. From the fact that Elisabeth is a scientist or Robert is not a soldier we can infer that if Robert were a soldier, then Elisabeth is a scientist via rewriting. From the fact that Robert is a soldier if and only if Elisabeth is a scientist we can infer that if Elisabeth were a scientist, then Robert is a soldier via biconditional elimination. From the fact that if Robert were a soldier, then Elisabeth is a scientist, and that if Elisabeth were a scientist, then Robert is a soldier we can infer that Robert is a soldier if and only if Elisabeth is a scientist via biconditional introduction. Finally, from the fact that Robert is a soldier if and only if Elisabeth is a scientist, and that Robert is not a soldier we can infer that Elisabeth is not a scientist via biconditional elimination. Therefore, the answer is yes.