1

It was amazing that infectious diseases which had proven invulnerable to drug treatment until then could be effectively treated.

It was amazing that infectious diseases which had been proven invulnerable to drug treatment until then could be effectively treated.

I know that the second sentence is wrong, and the first is correct, but why?

2

It is because when used in this context the verb

To prove

Means

To be found either by trial or by experience to be

http://www.dictionary.com/browse/proven

... infectious diseases which had proven invulnerable ...

... infectious diseases which had been found by experience to be invulnerable ...

Adding the verb to be makes it non-sensical because

... infectious diseases which had been proven ...

would become

... infectious diseases which had been been found by experience ...
0

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.

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