without a shadow of a doubt
without the/a shadow of (a) doubt
With certainty; for sure. I only made such a big change in my life because I knew without the shadow of a doubt that it was the right thing for me to do.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
without a shadow of a doubtand beyond the shadow of a doubt
without the smallest amount of doubt. I am certain that I am right, without a shadow of a doubt. I felt the man was guilty beyond the shadow of a doubt.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.