Time indepedendent Schrödinger equation for a system (atom or molecule) consisting of N electrons can be written as (with applying Born - Oppenheimer approximation): $$ \left[\left(\sum_{i=1}^N - \frac {h^2} {2m} \nabla _i ^2\right) + \sum_{i=1}^N V(r_i) + \sum_{i < j}^N U(r_i,r_j)\right] \Psi = E \Psi $$
Terms in Hamiltonian are as follows:
- Kinetic energy of electrons
- Potential energy of electron - nuclei interaction
- Potential energy of electron - electron interaction
It is said that for N electron system, kinetic energy of electrons and potential energy of electron - electron interaction are system independent which means that their value depends only on number of electrons $N$ (Because of that they are called universal operators). Potential energy of electron - nuclei interaction depends on specific system and isn't determined only by $N$.
Source: DFT wikipedia, section: Derivation and Formalism, 2nd paragraph.
https://en.wikipedia.org/wiki/Density_functional_theory.
Second source is this page where Hohenberg and Kohn theorems are proved; statements are made after equation 1.31.
http://cmt.dur.ac.uk/sjc/thesis_ppr/node12.html
Why is this? This is usually mentioned in DFT materials, but I didn't find any source which explains it.