LOL!
Heaven's no!
The States have the right to bear arms provisions too.
In Texas:
The Texas Constitution
Article 1 - BILL OF RIGHTS
Section 23 - RIGHT TO KEEP AND BEAR ARMS
Every citizen shall have the right to keep and bear arms in the lawful defense of himself or the State; but the Legislature shall have power, by law, to regulate the wearing of arms, with a view to prevent crime.
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If the federal Constitution was meant to cover the entire country, why are the Bill of Rights duplicated almost word for word in every State Constitution?
Why do the State Constitutions even exist?