In general case given a system it is impossible to prove it is not self-contradictory.
If you're asserting it, by merely asserting axioms, then (in the general case,) yes. If you're constructing it, and showing that the axioms are satisfied, then no: there are several ways to construct a model that nobody has ever found a contradiction in, and you can construct spherical geometry this way.
Comments
If you're asserting it, by merely asserting axioms, then (in the general case,) yes. If you're constructing it, and showing that the axioms are satisfied, then no: there are several ways to construct a model that nobody has ever found a contradiction in, and you can construct spherical geometry this way.
Is not a proof.