How come Rem in Death Note died by killing L?

Well, the one that all Shinigami's have to abide by, is that they CANNOT, on the pain of death, help humans. Meaning, that they cannot use any of their powers to benefit a human. Killing L, helped Misa because she really wanted to help Light. So, that's why Rem died. hope I helped. I don't exactly remember all the details, sorry, I read Death Note over a year ago...