beyond any doubt
Definitions
With absolute certainty; completely proven.
Without any possibility of being questioned or disputed.
Examples
The DNA evidence proved beyond any doubt that he was at the scene of the crime.
It is established beyond any doubt that regular exercise improves overall health.
Synonyms
indisputably unquestionably without a shadow of a doubt certainly beyond question definitely incontestably
Antonyms
dubiously questionably uncertainly debatably ambiguously vaguely possibly