a leg to stand on
Proof, defense, or support for one's argument or position. Often used in the negative to mean the opposite. The senator's company avoided paying millions in taxes over the years, so she doesn't have a leg to stand on when she criticizes tax dodgers. The truth is that the prosecution hasn't got a leg to stand on, now that their key witness was discredited in court. Why do I look so stressed? Perhaps because my thesis has no leg to stand on? Yep, the entire study was just retracted by a prestigious medical journal!
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