In verses 12-19 there is an emphasis on the fact that future resurrection of the dead is a consequence of Christ being raise. God's faithfulness assures this and therefore death will be defeated. Verse 12 poses the confusion rhetorically; if you became believers because you trusted the proclamation that Christ is alive, risen from the dead, how can you let people say that there is no living Christ. Christ died for our sins according to the scriptures, and was raised again according to scriptures. This then was the means of their salvation, if they continued in it, unless they had believed in vain. In verse 14 Paul mentions the consequence, if Christ is not risen , the preaching of the Gospel is in vain, and the credit that you gave to it is vain, and we are liars. Both Paul's preaching and their faith are empty if Christ has not been raised. The principal argument of the first preachers in support of Christianity was that God had raised Christ from the dead. If this fact were false, the faith built on it must be false too.
The apostles were chosen to be witnesses of the resurrection of Christ. He appeared to them, and was seen by them for this purpose. They were sent into the entire world, to bear their testimony to this truth, which they accordingly did. Now if Christ is not risen, they have born a false testimony. If they are false witnesses, they are false witnesses of God. The apostles must be bringing a false testimony from God, thus bearing a false testimony against him to say that he raise Christ from the dead, when he is not risen; which must be the case, if there is no resurrection of the dead.
It is even worse for those who died hoping in Christ and resurrection, because they're already in their graves. Those who are dead are represented by sleep, and have died in Christ, died in union with him, whether in the exercise of faith, or not. If Christ is not risen, they are now perished.