There is a straight line l 1 outside the plane A, which is parallel to a straight line in this plane, and l2 has an intersection point A with the plane.

Because l1/L2

So A is not on l2.

L 1, l2 defines a plane B.

A, l2 define the plane C.

Because a is on l 1

So plane b= plane C.

Because a and a, l2 are on plane a.

So plane b= plane c= plane a.

So l 1 is on plane a.

This contradicts the conditions.

So the assumption doesn't hold.

So if a straight line out of the plane is parallel to a straight line in this plane, then this straight line is parallel to this plane.