During his homily at today’s Mass, the priest talked about when he was in the seminary. He and his fellow seminarians were looking forward to the class on the Trinity, thinking that they would finally understand the Mystery of the Trinity. Indeed, the professor took them through all the teachings, Augustine, Aquinas, all the great philosophy and theology. At the end of the semester, the professor said: “There you have it, the Trinity: three persons, two processions, one God, zero proof.”
I take it the professor's comment relates to the objective of "finally understanding the Mystery of the Trinity." As to that, truly, "proof" of that which ultimately lies beyond our human comprehension is lacking. But that's not to say there isn't ample proof from Scripture and Tradition to affirm the Athanasian Trinitarian view as correct as against the competing viewpoints.