Can someone explain consensus theorem for boolean algebra In boolean algebra, below is the consensus theorem
$$X⋅Y + X'⋅Z + Y⋅Z = X⋅Y + X'⋅Z$$
$$(X+Y)⋅(X'+Z)⋅(Y+Z) = (X+Y)⋅(X'+Z)$$
I don't really understand it? Can I simplify it to 
$$X'⋅Z + Y⋅Z = X' \cdot Z$$
I don't suppose so. Anyways, why can $Y \cdot Z$ be removed?

Something like the following:
$X \cdot Y + X' \cdot Z + Y \cdot Z $ =
$X \cdot Y + X' \cdot Z + (X + X') \cdot Y \cdot Z $ =
$X \cdot Y + X \cdot Y \cdot Z + X' \cdot Z + X' \cdot Y \cdot Z$ =
$X \cdot (Y + Y \cdot Z) + X' \cdot (Z + Y \cdot Z)$ =
$X \cdot Y + X' \cdot Z$
