
theorem
  for X being set, x,y being object, R being symmetric Relation of X
  holds [x,y] in R implies [y,x] in R
proof
  let X be set, x,y be object, R be symmetric Relation of X;
  assume A1: [x,y] in R;
  then x in field R & y in field R by RELAT_1:15;
  hence thesis by A1, RELAT_2:def 3, RELAT_2:def 11;
end;
