From Pope Pius XII’s encyclical Mystici Corporis Christi (1943):
In the course of the present study, Venerable Brethren, we have thus far seen that the Church is so constituted that it may be likened to a body. We must now explain clearly and precisely why it is to be called not merely a body, but the Body of Jesus Christ. This follows from the fact that our Lord is the Founder, the Head, the Support and the Savior of this Mystical Body.
As We set out briefly to expound in what sense Christ founded His social Body, the following thought of Our predecessor of happy memory, Leo XIII, occurs to Us at once: “The Church which, already conceived, came forth from the side of the second Adam in His sleep on the Cross, first showed Herself before the eyes of men on the great day of Pentecost.”23 For the Divine Redeemer began the building of the mystical temple of the Church when by His preaching He made known His Precepts; He completed it when he hung glorified on the Cross; and He manifested and proclaimed it when He sent the Holy Ghost as Paraclete in visible form on His disciples.
For while fulfilling His office as preacher He chose Apostles, sending them as He had been sent by the Father24—namely, as teachers, rulers, instruments of holiness in the assembly of the believers; He appointed their Chief and His Vicar on earth;25 He made known to them all things and whatsoever He had heard from His Father;26 He also determined that through Baptism27 those who should believe would be incorporated in the Body of the Church; and finally, when He came to the close of His life, He instituted at the Last Supper the wonderful Sacrifice and Sacrament of the Eucharist.
23 Encycl. Divinum Illud: Acta Sanctæ Sedis, XXIX, p. 649.
24 John, XVII, 18.
25 Cf. Matth., XVI, 18-19.
26 John, XV, 15; XVII, 8 and 14.
27 Cf. John, III, 5.
— Mystici Corporis Christi 25-27