theorem Th74:
  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 that
    A1: t '=' u is LD-provable and
    A2: u '=' v is LD-provable;
  A3: u '=' t is LD-provable by A1, Th70, XBOOLE_1:7;
  set w = (u '=' v) '=' (t '=' v);
  (u '=' t) => w is LD-provable;
  then w is LD-provable by A3, Th62;
  hence thesis by A2, Th61;
end;
