reserve E,X,Y,x for set;
reserve A,B,C for Subset of E;

theorem
  (for a being Element of A holds a in B) implies A c= B
proof
  assume
A1: for a being Element of A holds a in B;
  let a be object;
  assume
A2:  a in A;
  reconsider a as set by TARSKI:1;
   a is Element of A by Def1,A2;
  hence thesis by A1;
end;
