But if it is preached that Christ has been raised from the dead, how can some of you say that there is no resurrection of the dead? If there is no resurrection of the dead, then not even Christ has been raised. And if Christ has not been raised, our preaching is worthless, and so is your faith. In that case, we are also exposed as false witnesses about God. For we have testified about God that He raised Christ from the dead
All Paul is doing is debunking the belief that sprouted up among the Christians back then that there is no resurrection of the dead with the logic that they already knew for a fact that Jesus was resurrected from the dead and that was a basis for faith in the resurrection of others too. In fact, the resurrection of Jesus is what they were preaching about.
(These guys back then weren't teaching from some book they read which was written some thousands of years ago. ( The Bible so states that:) This is something that they saw; they saw the resurrected Jesus; they saw Jesus ascend into heaven and Paul saw and communicated with Jesus. The resurrection of Jesus was proven conclusively to those witnesses and that is what these guys back then were witnessing and preaching about all over the place.)
They were testifying about what they saw and heard-not hearsay or something that they read off some book, and that is what being a witness is all about. The subject matter in the related "logic" is about debunking an erroneous conclusion that some had come to back then; Paul's logic is not about invalidating the resurrection, something proven (to them) to be true. Facts cannot be invalidated; neither with logic, not with arguments, not with other facts. Facts stand on their own and everyone back then was convinced for a fact that Jesus rose from the dead and no one could prove to them otherwise. And that proof was a basis for faith in the resurrection -not of Jesus- but of everybody else.