
theorem LEM2a:
  for X being set, R being Relation of X holds
    R /\ R~ is symmetric
  proof
    let X be set, R be Relation of X;
    (R /\ R~)~ = R~ /\ R~~ by RELAT_1:22
      .= R~ /\ R;
    hence thesis by RELAT_2:13;
  end;
