Golden Mean is Irrational

Theorem
The golden mean $\phi$ is irrational.

Proof
By definition of golden mean:
 * $\phi = \dfrac {1 + \sqrt 5} 2$

By Square Root of Prime is Irrational:
 * $\sqrt 5$ is irrational.

By Rational Number plus Irrational Number is Irrational:
 * $1 + \sqrt 5$ is irrational.

By Irrational Number divided by Rational Number is Irrational:
 * $\dfrac {1 + \sqrt 5} 2$ is irrational.