  This paper positively solves an open problem if it is possible to provide a
Hilbert system to Epistemic Logic of Friendship (EFL) by Seligman, Girard and
Liu. To find a Hilbert system, we first introduce a sound, complete and
cut-free tree (or nested) sequent calculus for EFL, which is an integrated
combination of Seligman's sequent calculus for basic hybrid logic and a tree
sequent calculus for modal logic. Then we translate a tree sequent into an
ordinary formula to specify a Hilbert system of EFL and finally show that our
Hilbert system is sound and complete for the intended two-dimensional
semantics.
