reserve E for non empty set;
reserve a for Element of E;
reserve A, B for Subset of E;
reserve Y for set;
reserve p for FinSequence;
reserve e, e1, e2 for Singleton of E;

theorem Th23:
  for E being finite non empty set, A,B being Event of E holds
  prob(A \ B) = prob(A) - prob(A /\ B)
proof
  let E be finite non empty set, A,B be Event of E;
  prob(A) = prob((A \ B) \/ (A /\ B)) by XBOOLE_1:51;
  then prob(A) = prob(A \ B) + prob(A /\ B) by Th21,XBOOLE_1:89;
  hence thesis;
end;
