I don't think it's needed to explain why or how it works to confirm it does work
It seems we run into that issue regularly with these "logic" questions. "Logic" isn't the ultimate answer to life and cannot provide complete explanations so we have to understand that. For better or for worse, however, some people cannot avoid getting embroiled in logic problems, and if they do they need to be pointed clearly to the way out, lest they give up and ruin philosophy for 2000 as did the namesake of the dialogue "Philebus."