beyond a shadow of a doubt

Prepositional phrase

Without any doubt or hesitation at all.

Japanese Meaning

一片の疑いもなく / 絶対に / 完全に確信して

The fingerprint evidence proved beyond a shadow of a doubt that he had been at the crime scene.

指紋の証拠は、彼がその犯罪現場にいたことを疑いの余地なく証明した。

Sense（1）

Without any doubt or hesitation at all.