Three friends or three strangers among six people

Six people are at a party; any two of them have either met before or not. Prove that you can always find three who have all met each other, or three of whom no two have met.

Pigeonhole on one person. Pick anyone, $P$. Of the other five, at least three share the same relation with $P$, say all have met $P$. If any two of those three have met, they form a trio of acquaintances with $P$; if not, those three are mutual strangers. The other case is symmetric.