Recently I have been very unsure of what really holds the probability theory together.

Often we say that if P(A)=0.88, then if we repeat an experiment in the long run, the event A will happen 88 % of the time. Is this a consequence of probability theory, or do we assume something else?

Do the law of large numbers tell us that probability and is the same as the long run relative frequency?

I am not sure what is a direct consequence of the 3 axioms we start out with, and what is not, but is often used?