The phrase "to prove why" is correct and usable in written English.
It can be used when you want to demonstrate the reasons or justifications for a particular argument or statement.
Example: "I will present the evidence to prove why this theory is valid."
Alternatives: "to demonstrate the reasons" or "to justify why".
It's not for the trans person to prove why she needs to use the female bathroom.
Students have to prove why they should be hired over others, but it still helps to be lucky.
The election programme is one of those moments when the corporation sets out to prove why it exists.
I went for the opposite approach, using science to prove why he was right (while actually achieving the opposite).
Why is it necessary to intrude on us, rather than burden us with the need to prove why they shouldn't?
After Mr. Droga was selected as one of the best and brightest for 2006 by Esquire magazine, the editors asked him to prove why his talent merited honoring.
Just to further prove why going back in time is a terrible idea, there is something called the grandfather paradox.
Anyone and everyone is DJ now so you have to earn your stripes so to speak, and prove why you're better than the next man, which encourages healthy competition.
"We want to go there and prove why we want to stay in League One and why they are probably going down to League Two," said Saddlers winger Jamie Paterson ahead of Walsall's trip, while Exeter boss Paul Tisdale admits the team are ready for life back in League Two.
Evidence of this plus is our inability to state the reasons and prove why we love the other even though we are certain of our love.
"We didn't play well, Aberystwyth were the better team and started well so we just had to go out there and prove why we are the champions and why we've got so much faith in the squad and team.
