From Pope Pius XII’s encyclical Mystici Corporis Christi (1943):
That [Christ] completed His work on the gibbet of the Cross is the unanimous teaching of the holy Fathers who assert that the Church was born from the side of our Savior on the Cross like a new Eve, mother of all the living.28 “And it is now,” says the great St. Ambrose, speaking of the pierced side of Christ, “that it is built, it is now that it is formed, it is now that it is . . . molded, it is now that it is created. . . . Now it is that arises a spiritual house, a holy priesthood.”29 One who reverently examines this venerable teaching will easily discover the reasons on which it is based.
And first of all, by the death of our Redeemer, the New Testament took the place of the Old Law which had been abolished; then the Law of Christ together with its mysteries, enactments, institutions, and sacred rites was ratified for the whole world in the blood of Jesus Christ. For, while our Divine Savior was preaching in a restricted area—He was not sent but to the sheep that were lost of the House of Israel30—the Law and the Gospel were together in force;31 but on the gibbet of His death Jesus made void the Law with its decrees32 fastened the handwriting of the Old Testament to the Cross,33 establishing the New Testament in His blood shed for the whole human race.34 “To such an extent, then,” says St. Leo the Great, speaking of the Cross of our Lord, “was there effected a transfer from the Law to the Gospel, from the Synagogue to the Church, from the many sacrifices to one Victim, that, as Our Lord expired, that mystical veil which shut off the innermost part of the temple and its sacred secret was rent violently from top to bottom.”35
28 Cf. Gen., III, 20.
29 Ambrose, In Luc, II, 87: Migne, Patrologiæ Cursus completus, Series Latina [P.L.], XV, 1585.
30 Cf. Matth., XV, 24.
31 Cf. St. Thos., I-II, q. 103, a. 3, ad 2.
32 Cf. Eph., II, 15.
33 Cf. Col., II, 14.
34 Cf. Matth., XXVI, 28; I Cor., XI, 25.
35 Leo the Great, Serm., LXVIII, 3: Migne, P.L. LIV, 374.
— Mystici Corporis Christi 28-29