Let $X$ be the blow-up of $\mathbb{P}^2$ at three general points $p_1,p_2,p_3$, that is a del Pezzo surface of degree six, and let $\pi_i:X\rightarrow\mathbb{P}^1$ be the morphism induced by the projection from $p_i$.

Does anyone know a reference for the following classical fact?

Any morphism $f:X\rightarrow\mathbb{P}^1$ factors through $\pi_i$ for some $i = 1,2,3$.