We can prove something (transitive). Through scientific method, we can demonstrate the truth of the thing.
Something can prove to be true or false or to possess a certain characteristic or identity. It is something whose truth or falsehood or whose characteristic or identity has become evident.
The passive is formed from the transitive, "we prove something": something has been proven (by someone) ...
Both the transitive and the intransitive accept a predicate complement, either in the form of the predicate adjective (true, false, some other attribute) or in the form of to be + adjective.
When an identity is expressed, we normally use to be:
The toxin proved to be arsenic.
The toxin was proven (by the forensic toxicologist) to be arsenic.
When a characteristic is expressed, we can choose the adjective alone or to be + adjective:
The climb proved difficult.
The climb proved to be difficult.