theorem Th18:
  for E,f,H,H9 holds E,f |= H => H9 iff (E,f |= H implies E,f |= H9)
proof
  let E,f,H,H9;
  E,f |= H '&' 'not' H9 iff E,f |= H & E,f |= 'not' H9 by Th15;
  hence thesis by Th14;
end;
