multi trait traits and building classes from classes

Im back again with another question.

if you take a trait with a trait with a "Rare traits X" ability and take a trait that is a Class only trait say lvl 1 and then build a lvl 2 class off that lvl 1 class how would the class only trait be handled?.

would you just remove the trait from the lvl 2 and the "Rare trait ability" only transfer the viable trait to the lvl 2?

or would you lose the class only trait and be able to pick a different viable one for the class lvl to replace it?

so example.

class lvl 1

scientific breakthrough 4pts: rare traits 2.

-example trait

-Example trait ( class lvl 1)

then you build a class lvl 2 from that class lvl 1