theorem
  for R being Relation holds y in Class (R,x) iff [x,y] in R
proof
  let R be Relation;
  thus y in Class(R,x) implies [x,y] in R
  proof
    assume y in Class(R,x);
    then ex z being object st [z,y] in R & z in {x} by RELAT_1:def 13;
    hence thesis by TARSKI:def 1;
  end;
A1: x in {x} by TARSKI:def 1;
  assume [x,y] in R;
  hence thesis by A1,RELAT_1:def 13;
end;
