What is Paul proving to the Corinthians about Christ?
The apostle is proving to the Corinthians, beyond a shadow of a doubt, that Christ genuinely died and then arose from the dead. That resurrection is the very hope of every believer; if Christ did not rise, the faith would be pointless, but the context affirms He did rise.
Les explains that this is what Paul is doing for the Corinthians: proving to them beyond a shadow of a doubt that Christ died, but that He arose from the dead. Les compares it to the story of a former infidel and college campus skeptic who went to Israel to dig up proof that the resurrection was a fallacy; instead, the more he dug, the more he proved himself wrong, and he came away a born-again believer. He then spent years going from college campus to college campus, proving to college kids that Christ literally, physically arose from the grave. Les says this resurrection is the very hope of every believer; if He didn't rise, we might as well pack up, throw our Bible away, go home, and forget it. But Les says don't do it, because He did arise from the grave.