Reference request: Projective representations of a simply connected real semisimple Lie group lift to unitary representations

Question

I recently got interested in representation theory in quantum mechanics and I read the following theorem:

Let $G$ be a simply-connected Lie group with $H^2(\mathfrak{g},\mathbb{R})=0$ and let $\mathcal{H}$ be a complex Hilbert space. Then every projective representation $\rho:G\to \text{Aut}(\mathbb{P}(\mathcal{H}))$ lifts to a unitary representation $\pi:G\to U(\mathcal{H})$.

I am looking for a proof of the theorem above, does anyone have a reference where it is proven?