Roman Catechism 6.6

Chapter 6 — Part I: The Creed — Article IV: Suffered Under Pontius Pilate, Was Crucified, Dead, and Buried

Section 6. "Was Crucified" — The fact that He suffered death precisely on the wood of the cross must also be attributed to a particular counsel of God, which decreed that life should return by the way whence death had arisen The serpent who had triumphed over our first parents by the wood (of a tree) was vanquished by Christ on the wood of the cross.