What I am doing now is making a hardwired ROM out of discrete logic gates, and part of my problem is that I am lacking enough knowledge of demorgans theorem.

I know the basics, but when I came to this site:

http://www.generalnumbers.com/demorgans_application1.html

It confused me a bit. It states that

AB + CD = ((AB)' (CD)')'

Now It is easy to prove it by drawing the logic gates out on paper.

But there has to be a way to prove it equation wise.

If so, can someone explain it to me without skipping a step?