This clever setup leverages a quirk in how copy effects interact with the searching process of Mirror-Mad Phantasm. Because Mirage Mirror is only a copy of the Phantasm until end of turn, it doesn't actually possess the name "Mirror-Mad Phantasm" while tucked away in your library. When you activate its ability, it shuffles itself in and searches endlessly for a card with that specific name, forcing you to mill your entire library in the process.