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 D being set, A being Subset of D st A is non trivial
    ex d1,d2 being Element of D st d1 in A & d2 in A & d1 <> d2
proof
  let D be set, A be Subset of D;
   assume A is non trivial;
    then consider d1,d2 being object such that
A1: d1 in A & d2 in A and
A2: d1 <> d2;
  reconsider d1,d2 as set by TARSKI:1;
    d1 in D & d2 in D by A1,Lm1;
    then reconsider d1,d2 as Element of D by Def1;
   take d1,d2;
   thus d1 in A & d2 in A & d1 <> d2 by A1,A2;
end;
