I have constructed truth tables to prove that:
$ABC + ABC'+ AB'C +A'BC = AB+AC+BC$

How do I prove it by simplifying the expression? I know that I can simplify: $ABC + ABC' = AB(C+C')=AB$. However I can't repeat this for $AB'C$ or $A'BC$, to get the answer I desire. 

I'm fairly new to boolean algebra and have tried to use the basic identities to figure it out, but can't seem to get there.