reserve R for Ring,
  I for Ideal of R,
  a, b for Element of R;
reserve R for add-associative right_zeroed right_complementable Abelian
    distributive left_unital non empty doubleLoopStr;
reserve I for Ideal of R;
reserve a,b for Element of R;
reserve x, y for Element of R/I;

theorem Th11:
  ex a being Element of R st x = Class(EqRel(R,I),a)
proof
  the carrier of R/I = Class EqRel(R,I) by Def6;
  then x in Class EqRel(R,I);
  then ex a being object
   st a in the carrier of R & x = Class(EqRel(R,I),a) by
EQREL_1:def 3;
  hence thesis;
end;
