本文通过一种易于理解但严格的定量计算证明了魏格纳旋转定理，得到了狭义相对论运动学不同方向速度合成的性质，并讨论了物理量的单调性与几种特殊情况，以便于读者形象直观地理解.基于这个定理，本文继续论证了狭义相对论体系的自洽性，并独立证明了原子物理与量子力学中涉及到的托马斯进动的结论.在大学教材体系对魏格纳旋转定理介绍较少的现状下，本文对本科生狭义相对论及量子力学的学习起到了补充作用.

This paper proves Wigner Rotation Theorem with a rigorous yet accessible calculation.It derives the properties of velocity composition in special relativity and discusses the monotonicity of physical quantities and several special cases for intuitive understanding.Based on this theorem, it demonstrates the internal consistency of special relativity and derives the conclusion on Thomas precession in atomic physics and quantum mechanics.Given the limited coverage of Wigner Rotation Theorem in textbooks, this paper supplements undergraduate learning in special relativity and quantum mechanics.