How do I simplify this boolean expression?
$
\begin{align}
ABC + ABC' + AB'C + A'BC = \\
ABC + ABC + ABC + ABC' + AB'C + A'BC =  &amp; &amp; &amp; \text{(2x Idempotency)}\\
AB(C + C') + ABC + ABC + AB'C + A'BC = &amp; &amp; &amp;\text{(Distribution)}\\
AB + ABC + ABC + AB'C + A'BC = &amp; &amp; &amp; \text{(Negation)}\\
AB + (AB + AB')C + (AB + A'B)C = &amp; &amp; &amp; \text{(2x Distribution)} \\
AB + (A(B+B'))C + ((A+A')B)C = &amp; &amp; &amp; \text {(2x Distribution)} \\
AB + AC + BC &amp; &amp; &amp; \text{(2x Negation)}
\end{align}
$

I'm not proficient at this kind of derivations so please correct any notation/terminology