I have Theorem, which states: Let $\mathcal{H}$ be Hilbert space with orthonormal basis $\mathcal{\varepsilon}=\{ e_i\}_1^{\infty}$ The following properties are equivalent:
1) $\epsilon$ is complet orthnormal basis for $\mathcal{H}$.
2) For ewery $x, y \in \mathcal{H}$: $$ \langle\,x,y\rangle=\sum_{i=1}^{\infty}\langle\,x,e_i\rangle \overline{\langle\,y,e_i\rangle} $$ 3) Parseval's equality: For ewery $x \in \mathcal{H}$: $$ ||x||^2=\sum_{i=1}^{\infty} |\langle\,x,e_i\rangle|^2 $$ How to prove that this 3 statements are equivalent?