Traditionally, the various semantics of the process algebra Csp are formulated in denotational style. For many Csp models, e.g., the traces model, equivalent semantics have been given in operational style. A Csp semantics in axiomatic style, however, has been considered problematic in the literature. In this paper we present a sound and complete axiomatic semantics for Csp with unbounded nondeterminism over an alphabet of arbitrary size. This result is connected in various ways with our tool Csp-Prover: (1) the Csp dialect under discussion is the input language of Csp-Prover; (2) all theorems presented have been verified with Csp-Prover; (3) Csp-Prover implements the given axiom system.