Axiom is a premise of reasoning solidly backed only by itself as sanctioned by experience. It is a self-evident statement; a proposition assumed to be true without the burden of proving it. And at times it is tried to be disproved, the attempt only presupposes its validity.
"I, this whole me, exist" is a classic example of a non-disprovable statement. It relies on the felt experience that it is so. And no other proof is necessary to assert that it is so. The attempt to disprove it, ie. the words "I don't exist", contradicts the very experience or feeling of being existent.
Perhaps existence is the grandest axiom forgotten as such. Everyone have this inherent feeling that he or she exists. This the deeply-rooted but supposed to be the most obvious feeling of presence, of being here, of being alive. But most are consumed in outward things like clothes, foods, friends, status, families, cosmetics, feelings, experiences. and worries that they forgot the very thing that makes everything possible - the fact of being here and now.
Men have forgotten that their true identity is the wholeness of everything at every moment. The cosmic amnesia has brought all sorts of suffering to humans. They strongly embrace the identity which they call "I" or "me". And with the act of keeping their identities intact comes the suffering brought by the struggle to keep it. And with this, everyday there goes the ego olympics where everyone is trying to outrun everybody else hoping that by doing such would make them fulfilled, loved by everybody, sought by everybody thus making the identity more solid and more self-fulfilling and leaving the fear of being left out at bay. Even worse is when one tries to outrun himself.
Existence is an axiom because it is as it is. The suffering felt can only be brought by the mistaken identity that we are discrete individual apart from everybody else. Apart from people around, apart from trees, from insects and animals, apart from falling leaves, from clouds, from dust and mud, from soil and rocks, from seas and river, from crimes and corruptions, from crooked politicians, from pious fellows, from gurus and students, from concrete blocks, from air, from oxygen and pollution, and literally apart from everything. However, if one comes to realization that everything at this moment is the perfect conspiracy of the wholeness itself, no more there will be a suffering brought by continuous struggle to keep the idea of "myself".
Even the idea that there is a Creator or God or gods that created the universe is no longer relevant if one understands the wholeness of everything. The concept of creator is not important except as a worthwhile alternative for men to keep in their heads while the axiomatic nature of existence is yet to be recognized. Once life is understood, that it is void of beginning and end, the idea about a God that is discretely apart from creation will vanish. What remains is the recognition that life is itself the very God we are trying to seek.
Struggle may bring something until you feel it is already boring struggling.