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

theorem Th2:
  (for x being Element of E holds x in A implies x in B) implies A c= B
proof
  assume
A1: for x being Element of E holds x in A implies x in B;
  let x be object;
  assume
A2: x in A;
  reconsider x as set by TARSKI:1;
  x in E by Lm1,A2;
  then x is Element of E by Def1;
  hence thesis by A1,A2;
end;
