theorem
  for t, u, v st t => u is LD-provable & u => v is LD-provable holds
      t => v is LD-provable
proof
  let t, u, v;
  assume A1: t => u is LD-provable & u => v is LD-provable;
  set x = LD-EqClassOf t;
  set y = LD-EqClassOf u;
  set z = LD-EqClassOf v;
  A2: LD-EqClassOf (t => u) = x => y & LD-EqClassOf (u => v) = y => z by Th97;
  LD-EqClassOf (t => v) = x => z by Th97;
  hence t => v is LD-provable by A1, A2, Th90, Th101;
end;
