Assuming that the straight line does not intersect with the plane, the axiomatic straight line is not in the plane, so the straight line is parallel to the plane;

Let L∪α= P

One ∈L, and one ∈! α (meaning does not belong)

On a, p is plane β, β∪α= PB,

Parallelism theorem from straight line to plane;

Straight AP// straight BP,

Two parallel lines AP and BP have an intersection, which is contradictory!

Therefore, the straight line AP intersects the plane α;