Hybrid EL-TBoxes combine general concept inclusions (GCIs), which are interpreted with descriptive semantics, with cyclic concept definitions, which are interpreted with greatest fixpoint (gfp) semantics. We introduce a proof-theoretic approach that yields a polynomial-time decision procedure for subsumption in EL w.r.t. hybrid TBoxes, and present preliminary experimental results regarding the performance of the reasoner Hyb that implements this decision procedure.