Proving the Eisntein equations imply the equivalence principle

lalbatros

One often read generalities about General Relativity and the Equivalence Principle.
The EP was a roadmap for building GR, clearly.
We are all convinced that the EP is embedded in GR.
Maybe we read a proof of it, sometimes ago.
But personally, I don't remember.

So, it would really be useful to me to learn how it can be seen precisely that the Einstein's equations imply the equivalence principle. I have the feeling that the covariance is the key, but I don't see the details.

Thanks for your lights,

Michel