Abstract calculi (tree transformation systems, term rewriting systems) express computational processes by transformation rules operating on abstract structures (trees). They have applications to functional programming, logic programming, equational programming, productions systems and language processors. We present proof of the Church-Rosser Theorem for a wide, useful class of abstract calculi. This theorem implies that terminating reductions always yield a unique reduced form in these calculi, which has the practical result that transformation rules can be safely applied in any order, or even in parallel. Although this result has previously been established for certain classes of abstract calculi, our proof is much simpler than previous proofs because it is an adaption of Rosser's new (1982) proof of the Church-Rosser Theorem for the lambda calculus.