'demonstrate the truth' is a correct and usable phrase in written English.
You can use it to refer to showing that something is true. For example, "In order to demonstrate the truth of his argument, John presented multiple evidence from reliable sources."
Three decades of data demonstrate the truth of that statement.
Politicians demonstrate the truth of this when they make decisions as parents rather than ministers.
As if to demonstrate the truth of his claim, he closed his bedroom door, went to the edge of his bed, and got down on his knees.
While Chelsea's players will have plenty of opportunities to demonstrate the truth of that old saying, their manager might be wondering if the opposite applies.
Here, on the day of an earlier jubilee in 1977, she has deputies who do the job more enthusiastically and demonstrate the truth of the metaphor on which the Queen's sovereignty depends.
If he gains the presidency, he will have ample opportunity to demonstrate the truth of that claim in a political culture that seems less and less able to find a middle ground.
Up to the section on prophecy (II.5), the discussion of each and every philosophical topic is followed by a section in which Ibn Daud provides biblical verses that are intended to point to or demonstrate the truths of the philosophical teachings in the preceding philosophical account.
And yet, for me, nothing demonstrates the truth of LP Hartley's line about the past being another country like the popularity of Formby.
From "Hagakure," the film quotes the standard Buddhist teaching "form is emptiness; emptiness is form," and Mr. Jarmusch sometimes seems intent on demonstrating the truth of this observation.
"My work is like a diary," Picasso often said, and Richardson demonstrates the truth of this in the third installment of his biography.
This has long been Horwitz's theme, and rather than simply explaining it, he demonstrates the truth of it, in story after story.
