logic: derive a formula using laws Let's say I have the following formula: 
$$(A\wedge\neg C)\vee(B\wedge C)\vee(A\wedge B).\tag{1}$$
It is easy to show following:
$$(A\wedge\neg C)\vee(B\wedge C)\vee(A\wedge B)\Leftrightarrow (A\wedge\neg C)\vee(B\wedge C).$$
What about deriving $(A\wedge\neg C)\vee(B\wedge C)$ from $(1)$ using Boolean algebra laws? (laws)

Using a more algebraic notation, one gets
\begin{align}
A\bar C + BC + AB &= A\bar C + BC + AB(C + \bar C) && \text{(Law $C + \bar C = 1$)}\\
&=A\bar C + BC + ABC + AB\bar C && \text{(Distributivity)} \\
&=(A + AB)\bar C + (B + AB)C&& \text{(Distributivity)} \\
&=A\bar C + BC&& \text{(Absorption)}
\end{align}
