Yes. It is commonly called FOPA. However, I am not sure where you got your version from, because I notice it says 178.38 at the front. Maybe you have the CFR (code of federal regulations version), I am not sure. This law is why we said it's no problem with your transporting the firearms. Notice what it says about ammo, if you are going to have any: it has to be controlled in exactly the same way as the firearm. Many people will tell you the firearm has to be separated from the ammo, IE carry the gun in the trunk and the ammo in the glovebox, or something like that, but that is illegal. The ammo must be controlled just like the firearm, and may even be in the same container as the firearm.
The most up to date version is 18 USC (United States Code) 926a:
TITLE 18--CRIMES AND CRIMINAL PROCEDURE
PART I--CRIMES
CHAPTER 44--FIREARMS
Sec. 926A. Interstate transportation of firearms
Notwithstanding any other provision of any law or any rule or
regulation of a State or any political subdivision thereof, any person
who is not otherwise prohibited by this chapter from transporting,
shipping, or receiving a firearm shall be entitled to transport a
firearm for any lawful purpose from any place where he may lawfully
possess and carry such firearm to any other place where he may lawfully
possess and carry such firearm if, during such transportation the
firearm is unloaded, and neither the firearm nor any ammunition being
transported is readily accessible or is directly accessible from the
passenger compartment of such transporting vehicle: Provided, That in
the case of a vehicle without a compartment separate from the driver's
compartment the firearm or ammunition shall be contained in a locked
container other than the glove compartment or console.