One of the shows I've been watching lately kept using some more classical forms of Japanese for style purposes, that I was not too familiar with ; this led me to notice how 得る{える} was often used as an auxiliary verb. For example, this makes constructions like 有り{あり}得ない{えない} way easier to remember now that I can see the how it's built.
Looking more into it, it seems (explained in here) that it can indeed be used to indicate potential as a somewhat old/formal form.
The modern potential form 〜られる/〜える looks very similar however (as alluded to in here), especially for godan verbs.
My hypothesis is that the modern 〜える (for godan verbs) directly comes from 得る, and that 〜られる (for ichidan verbs) was initially some kind of alternate construction (the only thing that comes to mind is a contraction of something involving ある like 食べれ・あれ・得る → 食べられる).
Is there any definite proof of the connection between the two? What transformations led to the construction of the modern form, if there is such a connection?