That's what the "Traditional" in "Traditional Christianity" means. Whatever actually happened, if anything, the companions of Christ believed that He died and then rose from the dead. QvQ quoted a passage from 1st Corinthians to that effect, probably the earliest statement we have of it. Scholars of all stripes generally agree that a person named Paul existed and wrote that letter to people in Corinth. Unless you suppose he was pulling their leg, he believed what he wrote and that was the beginning of the traditional belief that has been handed down to this day, that and the writings of others close to the original twelve. The documents themselves don't prove it, they only bear witness to the beliefs of the authors.
Alternatively, one could assert that the letter to the Corinthians was not written by Paul off his own bat but dictated in some way by God, in which case the resurrection is was not just Paul's belief but an objectively true statement. I have never cared very much for that point of view. After all, Christ's commission to us was "Preach the Gospel..."