reserve E,X,Y,x for set;
reserve A,B,C for Subset of E;
reserve x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 for Element of X;

theorem
  for X be non trivial set, x being Element of X
   ex y be object st y in X & x <> y
proof
  let X be non trivial set;
  let x be Element of X;
   consider d1,d2 being object such that
A1: d1 in X & d2 in X and
A2: d1 <> d2 by ZFMISC_1:def 10;
   x <> d1 or x <> d2 by A2;
  hence thesis by A1;
end;
