DNA strand displacement gates can be used to emulate arbitrary chemical reactions, and a number of different schemes have been proposed to achieve this. Here we develop modular correctness proofs for strand displacement encodings of chemical reaction networks and show how they may be applied to two-domain strand displacement systems. Our notion of correctness is serializability of interleaved reaction encodings, and we infer this global property from the properties of the gates that encode the individual chemical reactions. This allows correctness to be inferred for arbitrary systems constructed using these components, and we illustrate this by applying our results to a two-domain implementation of a well-known approximate majority voting system.