I suggest using propter with accusative.
With your example:
Propter theorema 5.6 functio est differentiabilis.
This Latin mathematical text by Gauss has several instances of propter, for example:
propter [...] seriei convergentiam — by convergence of the [...] series
propter has rationes — for these reasons
propter  — by equation 
The word theorema appears several times, but never in the sense of "by theorem", and lemma only appears as a title for two auxiliary results.
However, based on modern mathematical language and these examples from Gauss, it makes sense to me say propter lemma/theorema.
It might also be worthwhile to take a look at propter in L&S, especially II.B.1.