I'm trying to learn the Cox Proportional Hazards Model on my own, and found this link that describes it in clear terms. But when I get to Formula (5) ($S(t) = \exp(−H(t))$) I can't figure out where that's coming from. On the author's previous page, he shows that the survival function equals $S(t) = \exp(−H(t))$ if we assume an exponential distribution, but in Cox we don't assume that.
Is $S(t) = \exp(−H(t))$ something that works for any hazard distribution? I can't think of a way to prove/disprove this, and the intuition isn't making sense for me.