Proof of a point beween two different points. (Geometry)

Question

I'm struggling with some of the logic writing this proof. This is the question:

Prove that if X is in AB (AB is a line segment) with X =/= B, then dist(AX) < dist(AB).

Logically this makes perfect sense. The problem is that I struggle with putting it into words. This is my attempt.

Proof: Towards a contradiction, suppose that the distance AX >= AB. Then by definition, AX + XB >= AB. This implies that X is not in the line segment AB. =><=

Am I close or should I use a different approach?

Answer 1

Since $X \ne B$, $dist(X, B) > 0$.

Since $dist(A, X) + dist(X, B) =dist(A, B) $, $dist(A, X) =dist(A, B)- dist(X, B) < dist(A, B) $.