NO that is WRONG!!!!!
F or P = Full Far First Class
A = Dicsounted First Class (SUb Class Code)
In the booking system (lets say Sabre) It will usually show the following:
If a flight is getting full they will remove seats from the sub class first (eg. A)
A Class usually have more restrictions but when you are that far up it doesn't make much difference. But arrogant airlines such as AA
(sorry for the PUN!) when they have like 9 F Class seats left 2 hours before the flight, they will still hold you back and won't give it to you if you are on an A Class booking!