Complex sentence: The Merkle-Damgård construction has been proven to depend for its security only on the security of the used compression function, so we only need to show that the compression function\\ phi we gave is secure.
Split into simpler sentences: The Merkle-Damgård construction has been proven to depend its security only on the security of the used compression function. So we only need to show that the compression function\\ phi is secure.