This is an explanation of Yudkowsky's idea from the metaethics sequence. I'm just trying to make it accessible in language and length with lots of concept handles and examples.

Technically, you could believe that people are equally allowed to be enslaved. All people equal + it's wrong to make me a slave = it's wrong to make anyone a slave.

"All men are created equal" emerges from two or more basic principles people are born with. You might say: "Look, you have value, yah? And your loved ones? Would they stop having value if you forgot about them? No? They have value whether or not you know them? How did you conclude they have value? Could that have happened with other people, too? Would you then think they had value? Would they stop having value if you didn't know them? No? Well, you don't know them; do they have value?

You take "people I care about have value" (born with it) and combine it with "be consistent" (also born with), and you get "everyone has value."

That's the idea in principle, anyway. You take some things people are all born with, and they combine to make the moral insights people can figure out and teach each other, just like we do with math.