This paper presents a formal proof sequence deriving the three fundamental laws of Structure Theory from three basic axioms concerning existence, change, and stability of structured systems. Unlike purely empirical or speculative approaches, the axioms are grounded in universal observable principles about the nature of structure and its transformation. Using representative physical examples, a sand-water system, an ice cube, and a candle, the proof illustrates how structural changes manifest across different domains and how systems respond to disturbances depending on their stability and structural depth. The resulting laws describe the existence of a transformation threshold below which systems return to their original state, the inverse relationship between structural stability and susceptibility to change, and the permanence of changes affecting fundamental structural layers. This axiomatic derivation provides a logically necessary and empirically verifiable foundation for understanding structural transformation in natural and artificial systems, offering a unifying framework with broad interdisciplinary applicability.