Moral facts are logically derived from the (true) axiom that suffering is bad. HTFH.
What do you mean by bad? Morally bad? Please clarify. I'll assume you mean morally bad, while we await clarification.
You cannot explain what makes things morally bad by asserting that suffering is morally bad. If, for example, we say it is morally bad to abuse infants for one's own amusement because
human suffering is morally bad then we explain moral badness by appealing to moral badness, which is circular.
Suppose we say suffering is bad. Suppose others say suffering is good. How do we decide who is right? If we try to justify our view over and against the other's view then we admit our view cannot be axiomatic since axiomatic truths need no justification.