Proof-by-linking (PBL) is an interactive theorem proving technique that uses direct manipulation UI actions such as drag-and-drop to assert links between subformulas of the goal. These links are used by the system to rewrite the goal in a way that reflects the intention of the user performing the manipulation. Because PBL avoids the use of proof languages, the same technique can potentially be used as a frontend to any existing formal reasoning system, making PBL a universal interaction method. In this paper we substantiate this claim by showing how to extract formal proofs from PBL derivations in a variety of existing proof languages, using a variety of techniques including reflection, combinators, and meta-programming. Crucially, all our extraction procedures use the native notions of propositions/formulas in the target proof systems, which makes the PBL technique compatible with the existing proof building machinery in these systems. We also provide implementations of the extraction procedures in an extension of the Profint framework, which runs on the client side in any modern web-browser.