It is so important that he repeats himself and then applies it. If Christ was not raised, it is because he was crushed by the punishment of sin on Calvary.
What Paul is saying is that the resurrection shows us that Christ truly accomplished the atonement. If there had been no resurrection, it is open for us to imagine that perhaps Calvary was unsuccessful. What if after half an hour of bearing the tremendous crushing weight of sin for his people, even the Son of God was crushed? Or what if the Son of God called it to a halt, and wouldn't go on any further? The resurrection makes clear that none of that is true, because the one who suffered and died and went right through to the end rose again. That is the demonstration that Calvary was altogether successful.