theorem Th92:
  for x, y holds x '=' y is LD-provable iff x = y
proof
  let x, y;
  consider t, u such that
    A2: x = LD-EqClassOf t & y = LD-EqClassOf u and
    A3: x '=' y = LD-EqClassOf (t '=' u) by Def93;
  thus x '=' y is LD-provable implies x = y
    proof
    assume x '=' y is LD-provable;
    then t '=' u is LD-provable by A3, Th90;
    hence thesis by A2, Th80, Def76;
    end;
  assume x = y;
  then t '=' u is LD-provable by A2, Th80, Def76;
  hence thesis by A3;
end;
