Truth is proved when it is combined with humility.
When we think we know the truth and we are truthful, we generally tend to also have arrogance of that truth. This is why we argue and try to prove our point to the other person. We are not able to see what the other person has to say and continue to put forth our own idea or perspective. This sometimes leads to futile arguments and conflicts.
When I am truthful, I also have humility. With humility I am able to put forth my idea to the other person in a detached way. The truth in me will enable me to understand the other person accurately and will keep me open to see his point of view too. This naturally will get my point across without much of difficulty, as the other person is also able to see my point of view.