beyond a shadow of a doubt
US /biˈjɑːnd ə ˈʃædoʊ əv ə daʊt/
UK /biˈjɑːnd ə ˈʃædoʊ əv ə daʊt/

1.
without any doubt; certainly
:
•
She is, beyond a shadow of a doubt, the best candidate for the job.
•
The evidence proves beyond a shadow of a doubt that he is guilty.