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The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
The Tenth Amendment is generally recognized to be a truism. In United States v. Sprague the Supreme Court noted that the amendment "added nothing to the instrument [the Constitution] as originally ratified." That said, it makes explicit the idea that the federal government is limited only to the powers it is explicitly granted.
In United States v. Lopez, a federal law mandating a "gun-free zone" around and on public school campuses was struck down because there was no clause in the Constitution authorizing it. The opinion did not mention the Tenth Amendment.
See also
9th Amendment
United States Bill of Rights
United States Constitution11th Amendment