Once a line is parallel to a plane, cut through it with a plane and the line where they meet must be parallel to it.
Module goal. Master systematically the tests and properties of parallel lines, line-and-plane, and plane-and-plane, and learn to convert freely among them.
eastmath.com · 28.6 Parallelism in Space: Tests and Properties · 28.6.2 Property of a Line Parallel to a Plane