exist: (verb): to be, especially to be a real, actual, or current thing, not merely something imagined or written about.
legitimate: (adjective): complying with the law, or under the law; "derive(s) its powers from the consent of the governed".
If these are the definitions of these words, I will continue.
United States:
- Is real, actual, and current (current meaning near the present time).
- Derives its powers from the governed (or citizens), as in: voting, the House of Representatives, having a citizen in positions of power (not only royalty as leader), having court system and right to defend one's self in front of a jury, being able to take a president from his position (Richard Nixon).