The phrase "further proof of how" is correct and usable in written English.
You can use it when you want to introduce an additional example or piece of evidence to support a point. For example, "This evidence is further proof of how widespread the issue is."
The plight of Iraqis uprooted by violence is further proof of how broken the country is.
Further proof of how underappreciated Ray's genius and the Kinks' brilliance remain, despite a nearly 40-year career.
Lycos's top 10 fads of the year offered further proof of how far out of the loop I am.
Reacting to the murder of the British Labour MP Jo Cox, Kern said the incident was "further proof of how quickly violent words can turn into violent deeds".
"A vote for yet another job-killing expansion of government in the wake of newly released skyrocketing unemployment numbers would just be further proof of how politically tone-deaf the Democratic majority has become," said Ken Spain, the communications director of the National Republican Congressional Committee.
Experts said that the results of the survey, in which 253 of about 2,000 specialist psychiatrists working in Child and Adolescent Mental Health Services (CAMHS) care took part, are further proof of how poor NHS services are for the growing number of children and young people struggling with serious psychological and psychiatric illnesses.
In the end it was Clara's increasingly Doctor-ish nature needed in order to survive, and it was further proof of quite how much the character has changed.
If you need further proof of just how gridlocked and embarrassing Congress has become in recent years, consider this.
And if you need further proof of his impact on the sport, consider how many triathletes have been made an MBE.
Mr. Seminerio has not publicly responded to the charges, but his case is further proof of why public officials need to declare openly how they earn their private income.
And further proof of this phenomenon comes with Time magazine's latest issue, featuring a cover story headlined "How Trump won".
