It doesn't say that. Jesus preached the prophets. So did Peter and Paul and the apostles. And Peter's last words admonished the church to remember the words of the prophets. It means that the age of the prophets and writings from them ended with John. It doesn't mean that all of what they said had been fulfilled with John.
"Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil." -- Matthew 5:17