The Dual Theorem of Pappus; a special case

In P², let the line through L and L' be the line at infinity. Given lines a, b, c passing through a point L, and lines a', b', c' passing through a point L', then a, b, c are parellel lines, and similarly a', b', c' are also parellel lines. Let P be the line through the points (a ¡û b') and (a' ¡û b). Similarly let Q be the line through the poins (a ¡û c') and (a' ¡û c), and R be the line through the poins (b ¡û c') and (b' ¡û c). Then lines P, Q, R are coincident.