The proof consists of two parts (or steps).

Is consists of correct or it should be consists in instead ? and why ?


As this chart shows, in the construction [some complete thing] consists in [the parts thereof]...

...the preposition in is now at the very least "dated", and should probably be avoided in your own text. But of course some people will think old = traditional = authoritative, so you might still want to use it.

As pointed out in this ELU answer to a related question, there is a potential semantic distinction...

consist of - be composed or made up of
consist in - have as an essential feature

...but realistically not many people would recognize that today, and it's quite likely the distinction will be completely lost in the fullness of time. So my advice would be to stick with of for all contexts (even those people who still do know the difference are unlikely to think anything you write is "incorrect").

Having said all that, if you do want to use the less common form, here's an illustrative example...

Your support for me consists of backing me up when you happen to agree with me, and remaining silent if you don't. But true loyalty consists in actively supporting me even when you don't agree.

That's to say, there are lots of different kinds of "support", and consists of simply introduces those elements that comprise your support. But "true loyalty" is actually defined in a more general sense as being something that consists in the attributes specified.

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