Chinese Remainder Theorem

Given:
(1) There is exactly 1 single variable X
(2) There are moduli m_1, ... m_n
(3) m_1 to m_n are all relatively prime to each other
(4) for any a_1 to a_m  values

Then:
There is exactly 1 X that solves the equation  mod (m_1 * ... * m_n)