Given a smooth manifold $M$ and its differential graded commutstive de Rham algebra $(\Omega(M),d,\wedge)$, the wedge product $\wedge$ can be projected onto the de Rham cohomology $(H_{dR}(M),\wedge)$.
What is an elegant way to proof that the wedge product is, indeed, well defined on $H_{dR}(M)$?