Hi!. I have problems with this proof

Let $f: (x ,t_x)\longrightarrow{(y,t_y)}$ , $B_x$ base of $t_x$ and $B_y$ base of $t_y$

I have to prove that

$f$ is continuous $\Longleftrightarrow{\forall{B\in{B_y}}}, \exists{B^{\prime}\in{B_x}} | B^{\prime}\subseteq{f^{-1}(B)}$

Continuous of functions (definition)

Let $X$ and $Y$ be topological spaces. A function $f: X\longrightarrow{Y}$ is said to be continuous if for each open subset $V$ of $Y$, the set $f^{-1}(V)$ is an open subset of X