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sledge-hammer argument

A strong argument that eliminates all opposition. I really want to win the debate next week, so I'm preparing a real sledge-hammer argument.
See also: argument

use a sledgehammer to crack a nut

  (British & Australian)
to do something with more force than is necessary to achieve the result you want
Usage notes: A sledgehammer is a large, heavy tool with a wooden handle and a metal head that is used for hitting things.
Sending ten men to arrest one small boy was a clear case of using a sledgehammer to crack a nut.
See also: crack, nut, sledgehammer, use