a shred of doubt

A modicum of doubt; the slightest bit of uncertainty. This photo now proves, without a shred of doubt, that my client is innocent. I witnessed the murder firsthand, so I don't have a shred of doubt that he is the one to blame. I barely remember leaving the office last night, so I can't say beyond a shred of doubt that I set the alarm before I left.

without a shred of doubt

Absolutely or with absolute certainty; with no doubt whatsoever. This photo now proves, without a shred of doubt, that my client is innocent. He made the accusation without a shred of doubt in his voice. This is without a shred of doubt the best movie of the year, perhaps even the decade.