Quotient of Lie Group by its universal representation Kernel has a faithful representation

Question

If $G$ is a connected Lie group then its linearizer $\Lambda$ (or universal representation kernel) is defined as the intersection of all the kernels of all continuous finite dimensional representations of $G$. It is a theorem of Goto that $G/\Lambda$ has a faithful representation but the proof is quite long. Does anyone know a simpler proof in the case where $G$ is semisimple?