
theorem
  for x,y being object holds ({[x,y]} qua Relation)~ = {[y,x]}
proof
  let x,y be object;
  set Z = ({[x,y]} qua Relation)~;
  now
    let a,b be object;
    hereby
      assume [a,b] in Z;
      then [b,a] in {[x,y]} by RELAT_1:def 7;
      then [b,a] = [x,y] by TARSKI:def 1;
      then b = x & a = y by XTUPLE_0:1;
      hence [a,b] in {[y,x]} by TARSKI:def 1;
    end;
    assume [a,b] in {[y,x]};
    then [a,b] = [y,x] by TARSKI:def 1;
    then a = y & b = x by XTUPLE_0:1;
    then [b,a] in {[x,y]} by TARSKI:def 1;
    hence [a,b] in Z by RELAT_1:def 7;
  end;
  hence thesis by RELAT_1:def 2;
end;
