Paradoxically, if the plane α of AC and BD is assumed, then A, B, C and D are all in the plane α. a，B ∈a，C，D ∈ B。

So a∏α and b ∏α; It is contradictory that the * * * plane α of A and B and A and B are straight lines in different planes. So the assumption is wrong, so that AC and BD are straight lines in different planes.