The rule of law was an outline incorporating numerous principles, the core of which was that no person was above the law.
The rule of law was upheld in the United Federation of Planets. When Commander Bruce Maddox challenged Lieutenant Commander Data's right to resign from Starfleet in 2365, Maddox alleged he had a right not to have his work on cybernetics subverted. However, Captain Phillipa Louvois, who was hearing the matter, noted that the rule of law would forbid the seizure of people for experimentation. (TNG: "The Measure Of A Man")
When trapped in a telepathic reality in 2373, Odo was confronted with a representation of his past self appearing as Odo's predecessor Thrax. "Thrax" argued that "When your people resort to terrorism and violence, they're fighting against order... against stability... against the rule of law, and that must stop." Odo, remembering that his attitude had condemned four innocent Bajorans to death, replied that there was more to life than the rule of law. (DS9: "Things Past")
After The Doctor was illegally sold by Gar to be put to work on the Dinaali Hospital Ship 4-2 in 2377, he protested his illegal detainment, and inquired whether or not the rule of law had reached that society yet. He was nevertheless told by Chellick that he was being used per the Allocator's rules, and was placed to work on "Level Blue." (VOY: "Critical Care")