Besides a copy of the TSA rules, print out a copy of the LAW! Sometimes "they" have to be forced to comply. Happened to me at RDU.
Electronic Code of Federal Regulations
e-CFR data is current as of April 27, 2018
Title 49 → Subtitle B → Chapter XII → Subchapter C → Part 1540 → Subpart B → §1540.111
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Title 49: Transportation
PART 1540—CIVIL AVIATION SECURITY: GENERAL RULES
Subpart B—Responsibilities of Passengers and Other Individuals and Persons
§1540.111 Carriage of weapons, explosives, and incendiaries by individuals.
(a) On an individual's person or accessible property—prohibitions. Except as provided in paragraph (b) of this section, an individual may not have a weapon, explosive, or incendiary, on or about the individual's person or accessible property—
(1) When performance has begun of the inspection of the individual's person or accessible property before entering a sterile area, or before boarding an aircraft for which screening is conducted under this subchapter;
(2) When the individual is entering or in a sterile area; or
(3) When the individual is attempting to board or onboard an aircraft for which screening is conducted under §§1544.201, 1546.201, or 1562.23 of this chapter.
(b) On an individual's person or accessible property—permitted carriage of a weapon. Paragraph (a) of this section does not apply as to carriage of firearms and other weapons if the individual is one of the following:
(1) Law enforcement personnel required to carry a firearm or other weapons while in the performance of law enforcement duty at the airport.
(2) An individual authorized to carry a weapon in accordance with §§1544.219, 1544.221, 1544.223, 1546.211, or subpart B of part 1562 of this chapter.
(3) An individual authorized to carry a weapon in a sterile area under a security program.
(c) In checked baggage. A passenger may not transport or offer for transport in checked baggage or in baggage carried in an inaccessible cargo hold under §1562.23 of this chapter:
(1) Any loaded firearm(s).
(2) Any unloaded firearm(s) unless—
(i) The passenger declares to the aircraft operator, either orally or in writing, before checking the baggage, that the passenger has a firearm in his or her bag and that it is unloaded;
(ii) The firearm is unloaded;
(iii) The firearm is carried in a hard-sided container; and
(iv) The container in which it is carried is locked, and only the passenger retains the key or combination.