Borel $\sigma$-field on $\mathbf{R}^{n}$ then Prove $\sigma(\pi (\mathbf{R} ))\ =\ \mathbf{B} (\mathbf{R} )$

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I know that the $\sigma$-field generated by the class of all open subsets of $\mathbf{R}$.

I want to show that a field generated by $\pi (\mathbf{R} )$ is the Borel $\sigma$-field ( $\mathbf{B} (\mathbf{R} )$) on $\mathbf{R}$.

i.e. $(\pi (\mathbf{R} ))\ =\ \ \sigma (\pi (\mathbf{R} )$

considering $\pi (\mathbf{R} ))\ =\ \{ (-\infty ,a]\ :\ a\ \varepsilon \ \mathbf{R} )$

I read that I need to show $\mathbf{B} (\mathbf{R} )\ \subseteq \ \sigma (\pi (\mathbf{R} ))$

But I need more insight.