If three skew lines all meet three other skew lines, any transversal to the first set of three meets any transversal to the second set of three.
Gallucci's Theorem
See also
Skew Lines, Transversal LineExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Gallucci's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GalluccisTheorem.html