reserve F,H,H9 for ZF-formula,
  x,y,z,t for Variable,
  a,b,c,d,A,X for set;
reserve E for non empty set,
  f,g,h for Function of VAR,E,
  v1,v2,v3,v4,v5,u5 for Element of VAL E;

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;
