$Vert x_{n} - y_{n} Vert $is a cauchy sequence in $mathbb{F}$

Given $X$ is a normed linear space over the field $mathbb{F}$ and $(x_{n}), (y_{n})$ be Cauchy seuqences in $X$ then $Vert x_n – y_n Vert$ is a Cauchy sequence in $mathbb{F}$ and consequently the $lim_{nrightarrow infty} Vert x_n -y_nVert$ exists

I know that this can be stated using the triangle inequality but I am not able to see how to use it here