Independency of a set in matroid theory

Question

Suppose $M=(X,I)$ be a matroid , $X=\{x_1,...,x_m\}$ and $$Y=\{x_i\mid \operatorname{rank}(\{x_1,...,x_i\}) > \operatorname{rank}(\{x_1,...,x_{i-1}\}) \}$$ then $Y$ is in I.

Could anyone help me with this problem? Thanks for any helps.