I don't want to go into too much detail as the situation could be quite revealing.
My line manager has said something which were completely out of order and very discriminating.
I had planned to stay quiet until I could prove the situation as he has this wonderful ability to lie his way out of any situation but it's causing a lot of stress, I'm not sleeping properly and it's on my mind all the time.
No you don't need 'proof', no. Grievance/disciplinary decisions in a workplace are not like in a court of law, there is no burden of proof equivalent to 'beyond unreasonable doubt'. In an extreme example, there is case law demonstrating that if an employer knows one of several people is stealing but cannot absolutely prove which one it is, it could be perfectly lawful to dismiss all of them. Not fair as such, to the innocent parties, but my point is you don't have to absolutely prove things.
Neither is it the case that if something is only witnessed by the two people concerned a grievance about it 'cannot' be upheld. Grievances are frequently upheld without third parties having witnessed incidents. An employer needs to take everything into account and decide on balance of probability whether something did or did not happen.
If someone is the subject of several individual complaints of sexual harassment, for example, demonstrating a pattern of behaviour, but without witnesses to any of it, an employer could uphold a grievance, and in fact would be failing in their duty of care just to wash their hands of it and do nothing unless and until the person did something with a third party eyewitness.
That's not to say that a complaint would necessarily result in disciplinary proceedings/a sanction in your particular case OP, but even if there isn't enough for that on this occasion, getting things on the record can be vital to form a pattern of events which might result in something/help someone else at another time, and/or might send the individual a warning shot that future incidents will be reported also so it would be sensible for him to therefore rein it in. What I mean is if reporting it does or might result in improving his conduct, that's worth doing in itself.