It seems that to prove this statement, you cannot assume the notion of true or false, otherwise its circular, meaning that the proof contains no reference to the concepts of true or false.
This invites a new definition of proof (maybe?), lets say, we need to show "truth exists" with absolute certainty.
But, does absoloute certainty exist? To prove it does, we cannot use notions of certainty, or truth or falsity, since that would be circular, so we must again re-define the notion of proof,
But this will go on for infinity, so any proof will be infinite regress. Hence anything you say with a notion of true or false, will require infinite regress, circular reasoning or assumptions?