Since $\mathcal{G}$ is a sigma-algebra on $\Omega$, then $\Omega \in \mathcal{G}$. Since $\mathbb{E}(X \mid \mathcal{G})$ is a conditional expectation of $X$ given $\mathcal{G}$ and since $\Omega \in \mathcal{G}$, then \begin{equation} \mathbb{E}(\mathbb{E}(X \mid \mathcal{G})) = \mathbb{E}(\mathbb{E}(X \mid \mathcal{G}) I_{\Omega}) = \mathbb{E}(X I_{\Omega}) = \mathbb{E}(X) \end{equation} $\square$