Meissel-Mertens constant in terms of the Euler-Mascheroni constant

Theorem

The following formula holds: $$M=\gamma + \displaystyle\sum_{p \leq n;p \mathrm{\hspace{2pt} prime}} \left[ \log \left( 1 - \dfrac{1}{p} \right) + \dfrac{1}{p} \right],$$ where $M$ denotes the Meissel-Mertens constant, $\gamma$ denotes the Euler-Mascheroni constant, and $\log$ denotes the logarithm.