Orthogonal Complement of Orthogonal Complement equals to closure of span

Question

Let $X$ is any inner product space and $A \subset X$

Show that $A^{\bot \bot} = \overline {spanA}$ (closure of $spanA$)

I should show $A^{\bot \bot} \subseteq \overline {spanA}$ and $A^{\bot \bot} \supseteq \overline {spanA}$

I have tried to use sequences for $A^{\bot \bot} \supseteq \overline {spanA}$ side but I couldn’t use. I’m really stuck. I need any help. Thanks in advance