Cycle Matroid is Matroid

Theorem
Let $G = \struct{V,E}$ be a graph.

Let $\struct{E, \mathscr I}$ be the cycle matroid of $G$.

Then $\struct{E, \mathscr I}$ is a matroid.

Proof
It needs to be shown that $\mathscr I$ satisfies the matroid axioms $(I1)$, $(I2)$ and $(I3)$.