theorem
  for E,f,H,H9 holds E,f |= H <=> H9 iff (E,f |= H iff E,f |= H9)
proof
  let E,f,H,H9;
  E,f |= (H => H9) '&' (H9 => H) iff E,f |= H => H9 & E,f |= H9 => H by Th15;
  hence thesis by Th18;
end;
