Contrary to Thomas Aquinias, you cannot prove it. That's kind of the point. Faith is also a matter of supernatural God-given enabling grace, without which no one would believe. But none of this defeats the Trilemma, either, if that's what you are trying to imply. Jesus' claims must be grappled with one way or the other.
Claims are linguistic, hence subject to logical analysis.
This is the nature of language, and it is inescapable. The only way to escape the reality of logic is to remain silent or grunt like apes. Discount yourself if you're too weak to take it on that basis. I see that we perhaps agree on this score, then. Thanks for the food for thought.