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 Th29:
  for E being finite non empty set, A,B,C being Event of E holds
  prob(A \/ B \/ C) = ( prob(A) + prob(B) + prob(C) ) - ( prob(A /\ B) + prob(A
  /\ C) + prob(B /\ C) ) + prob(A /\ B /\ C)
proof
  let E be finite non empty set, A,B,C be Event of E;
  prob(A \/ B \/ C) = prob(A \/ B) + prob(C) - prob((A \/ B) /\ C) by Th20
    .= ( ( prob(A) + prob(B) ) - prob(A /\ B) ) + prob(C) - prob((A \/ B) /\
  C) by Th20
    .= ( prob(A) + prob(B) + prob(C) ) + -prob(A /\ B) - prob((A /\ C) \/ (B
  /\ C)) by XBOOLE_1:23
    .= ( prob(A) + prob(B) + prob(C) ) + -prob(A /\ B) - ( prob(A /\ C) +
  prob(B /\ C) - prob((A /\ C) /\ (B /\ C)) ) by Th20
    .= ( prob(A) + prob(B) + prob(C) ) + -prob(A /\ B) - ( prob(A /\ C) +
  prob(B /\ C) - prob(A /\ ( C /\ (C /\ B)) )) by XBOOLE_1:16
    .= ( prob(A) + prob(B) + prob(C) ) + -prob(A /\ B) - ( prob(A /\ C) +
  prob(B /\ C) - prob(A /\ (( C /\ C ) /\ B) )) by XBOOLE_1:16
    .= (( prob(A) + prob(B) + prob(C) ) + -prob(A /\ B)) - ( prob(A /\ C) +
  prob(B /\ C) - prob(A /\ B /\ C) ) by XBOOLE_1:16
    .= ( prob(A) + prob(B) + prob(C) ) + -( prob(A /\ B) + prob(A /\ C) +
  prob(B /\ C) ) + prob(A /\ B /\ C);
  hence thesis;
end;
