Let $V$ be a real Hilbert space and $a:V\times V\to \mathbb{R}$ be continuous and coercive: $|a(u,v)|\le M\|u\|_V\|v\|_V$ and $a(v,v)\ge \alpha\|v\|_V^2$ for some $\alpha>0$. Then for every $F\in V^*$ there exists a unique $u\in V$ such that $a(u,v)=F(v)$ for all $v\in V$.