The phrase "an example to prove" is correct and usable in written English.
It can be used when you want to provide a specific instance or case that supports a claim or argument you are making.
Example: "To illustrate my point about the importance of exercise, I have an example to prove that regular physical activity can significantly improve mental health."
Alternatives: "a case to demonstrate" or "an instance to illustrate".
As an example to prove to people that God is still alive.
Although Gala apple, a very challenging case, is used in this paper as an example to prove its feasibility, this method could be easily adapted for other stone fruits.
Finally, we give an example to prove our main conclusion.
(P value: 0.8775). If you wanted an example to prove the old saw that data more than the plural of anecdote, you couldn't find a better one.
Mike Wallace ended his talk at the banquet on a positive note: People can change, he insisted, and gave an example to prove it.
While the NCTE might be using Petosky as an example to prove their point, she claims that she didn't want to be the subject of a media firestorm when she started talking about her experience on social media.
The EU Commission is mainly given as a good example to prove how an EU structure might be an influential platform for the process of Europeanization; however, national governments have the power to determine the nominees for the Commission and the commissioners were mainly selected from people with a good career in their national system (Thomson, 2011).
Further stressing presidential power, Gore gave a recent example to prove that a unilateral strike into a sovereign country to destroy dangerous weaponry is well within international law.
Last year, in a rare freak-everyone-out Wall Street Journal OpEd in support of improved cybersecurity legislation, President Obama resorted to an imaginary example to prove his point.
All the developed results are shown in terms of LMIs and tested on an illustrative example to prove the feasibility and applicability of the proposed method.
Fabry disease offers an exquisite example to prove the usefulness of chemico-physical methods for medicine.
