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
  for E being finite non empty set, A,B being Event of E holds prob(A) =
  prob(A \/ B) - prob(B \ A)
proof
  let E be finite non empty set, A,B be Event of E;
  prob(A \/ (B \ A)) = prob(A \/ B) by XBOOLE_1:39;
  then prob(A \/ B) = prob(A) + prob(B \ A) by Th21,XBOOLE_1:79;
  hence thesis;
end;
