that's the core that survived, yeah. but it's documented, that as early as marcion (~85-160) many (in some parts of the world the majority of) christians didn't believe in the resurrection story.
There was a reason that Marcion was viewed as a heretic and went on the create his own "church" and that wa sbecause his viewes were NOT shared by the majority of Christians.
The resurrection IS Christianity, without it there is no Christianity.
Paul makes his case by saying for those that doubt to question the eye witnesses to Christ being alive and there were quiet a few according to Him:
15 Now I would remind you, brothers and sisters, a of the good news b that I proclaimed to you, which you in turn received, in which also you stand, 2 through which also you are being saved, if you hold firmly to the message that I proclaimed to you—unless you have come to believe in vain.
3 For I handed on to you as of first importance what I in turn had received: that Christ died for our sins in accordance with the scriptures, 4 and that he was buried, and that he was raised on the third day in accordance with the scriptures, 5 and that he appeared to Cephas, then to the twelve. 6 Then he appeared to more than five hundred brothers and sisters c at one time, most of whom are still alive, though some have died. d 7 Then he appeared to James, then to all the apostles. 8 Last of all, as to one untimely born, he appeared also to me. 9 For I am the least of the apostles, unfit to be called an apostle, because I persecuted the church of God. 10 But by the grace of God I am what I am, and his grace toward me has not been in vain. On the contrary, I worked harder than any of them—though it was not I, but the grace of God that is with me. 11 Whether then it was I or they, so we proclaim and so you have come to believe.
Paul is basically saying, find out for yourself if you don't believe me, ask those that saw and were there.