Exactly, thanks VDJ.
The school I trained at had a MMA fight team that was based on TKD, BJJ blended with skills from other martial arts such as Muay Thai and boxing. The last school I was at also had a MMA fight team and they based theirs on Muay Thai and BJJ. Each were taught separate for an hour and then MMA trained as a whole for an hour; 3 hours total.
What are TMAs? They are skills that somebody decided to train in a certain manner and then they called it a name; names we are familiar with and have been around for a long long time. MMA is newer but it is the same thing, somebody decided to train particular skills. It doesn't matter what those skills are or what TMA they were taken from, it is just a matter of taking what is felt best to make a fighter better. Whereas TMAs are not predominately focused towards fighters, MMA more so is but even now schools of MMA are around that are not geared for fighting but to train a person self defense and discipline; just like TMAs. Therefore MMA is a form of martial arts.
Hence Bruce Lee's Jeet Kune Do