Proof Revision!

Take a look at the following proof.

We're going to try to prove that if $O$ is a point inside $\triangle ABD$, then $AD+AB>OD+OB$.

First join $O$ and $A$.

From the triangle inequality,

$AD+OA> OD\cdots (1)$

$OB+OA>AB\cdots (2)$

Subtract $(2)$ from $(1)$ to get,

$AD-OB>OD-AB$

Switch sides to get,

$AD+AB>OD+OB$

$\mathbb{QED}$

Here are some comments about the proof.

$[1]$. The proof is not correct. There's an invalid move hiding in there somewhere.

$[2]$. Relax! Not everything in this set is a trick question. This proof is perfectly fine.

$[3]$. Forget the proof! The claim itself is not true!

Which comment here is correct?

This problem is from the set "MCQ Is Not As Easy As 1-2-3". You can see the rest of the problems here.