Linear_Transformation_VS_Monomorphism

Let $G$ and $H$ be a $K$-vector space. Let $\phi: G \to H$ be a linear transformation. Then $\phi$ is a monomorphism for every linearly independent sequence $\sequence {a_n}$ of vectors of $G$, $\sequence {\map \phi {a_n} }$ is a linearly independent sequence of vectors of $H$.