I think that the apostle Paul is not talking about faith in general terms. Indeed we can have faith in many things. Rather he is speaking about "THE" faith. Our faith in Jesus Christ and his resurrection, which presupposes that He died and was buried. He died for our sins and He rose again for our justification. What the apostle is saying therefore is, that if Christ did not rise from the dead, then this would mean that God did not accept his sacrifice on the cross for our sins. The resurrection was God's seal that he had accepted Christs death as payment for our sins. For he was set forth to be a propititiation (to quell God's wrath against sin) for our sins.
And if God did not accept his sacrifice, then that would mean that our sins have not been paid for on the cross. The very fact that it was not possible that death could hold him and that he rose from the dead, means that he triumphed over death and therefore was victorious over the last enemy that was death.
So our salvation all hangs on whether Christ rose from the dead. So if he did not rise from the dead, then our faith in his resurrection would mean nothing. It would be a vain thing. The word "vain" here means "worthless". That is why we defend the doctrine of the resurrection so vigorously. Because it is the pivotal point of "THE" faith, our faith. And that is why the opponents of the Christian faith try to demolish the doctrine of the resurrection of Christ. Because if anyone could disprove that, then they would destroy the whole of the Christian gospel and would make it "worthless". For if Christ did not rise from the dead, then this would also mean that the whole of God's plan for the salvation of the world and His victory over sin and death and hell and the wicked one himself, would all fall flat and all things would perish entirely.
raying: