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 Th39:
  for E being finite non empty set, A,B being Event of E st 0 <
  prob(A) & 0 < prob(B) holds prob(A) * prob(B, A) = prob(B) * prob(A, B)
proof
  let E be finite non empty set, A,B be Event of E;
  assume that
A1: 0 < prob(A) and
A2: 0 < prob(B);
  prob(A) * prob(B, A) = prob(A /\ B) by A1,XCMPLX_1:87;
  hence thesis by A2,XCMPLX_1:87;
end;
