Beyond the shadow of a doubt, or beyond a shadow of a doubt, is a standard of proof. The phrase means the issue in question is so obvious, or has been so thoroughly proven, that there can exist no doubt.
双语例句
1
The most important feature of James’s work was that he proved beyondashadow of a doubt that an extremely important function of leadership is motivation.
詹姆士的作品有个最重要的特点，就是他无庸置疑地证明了领导者有个极为重要的作用，那就是激励作用。
2
The origin of Tuesday's attack is identified beyondashadow of doubt.
周二的攻击来源无疑是确定的。
3
Remember that you don't need to get to the point of "beyondashadow of a doubt" when judging people.