Prince William said Tedworth House made him and his brother, Prince Harry, "very, very proud" as he declared the recovery centre officially open.
He said: "It is an enormous pleasure to be here at Tedworth House. This place, and what Help for Heroes and its partners have done here, makes Harry and me very, very proud."
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A Labrador had a miraculous escape after surviving a 150-foot plunge down a cliff on Christmas Day.
Passengers, including a pregnant woman, say they have been stranded since 4pm yesterday.
The boxer said it was the "least he could do" and even donated the £30,000 shorts he wore in his last fight against Devon Alexander.