Le Doux is quite correct. A "vestibule" is a small room at the entrance of a building to protect the innards from the weather, (note the same as described for your camping tent, Brian.)
A small room leading to a larger room (as on the second floor of the TSBD) is an "ante room".
Just for you, Brian, (sorry, Dougal.)
It shows, Mr Mitcham, the utterly pitiable state of Anti-Prayer-Man research that the Anybody-But-Oswald zealots' case rests on
---------------murdering normal dictionary definitions of words!
---------------arguing that Prayer Man is a white-haired woman!
---------------arguing that left is right!
---------------interpreting 'Then went outside to watch P. parade' as meaning something other than 'Then went outside to watch Presidential parade'!
These people recall the glory days of Mr Cinque!