theorem Th80:
  for t, u holds t LD-= u iff LD-EqClassOf t = LD-EqClassOf u
proof
  let t, u;
  thus t LD-= u implies LD-EqClassOf t = LD-EqClassOf u
    proof
    assume t LD-= u;
    then [t, u] in LD-EqR by Def80;
    then u in LD-EqClassOf t by EQREL_1:18;
    hence thesis by EQREL_1:23;
    end;
  assume LD-EqClassOf t = LD-EqClassOf u;
  then u in LD-EqClassOf t by EQREL_1:23;
  then [t, u] in LD-EqR by EQREL_1:18;
  hence thesis by Def80;
end;
