61 In a natural body the principle of unity unites the parts in such a manner that each lacks in its own individual subsistence; on the contrary, in the Mystical Body the mutual union, though intrinsic, links the members by a bond which leaves to each the complete enjoyment of his own personality. Moreover, if we examine the relations existing between the several members and the whole body, in every physical, living body, all the different members are ultimately destined to the good of the whole alone; while if we look to its ultimate usefulness, every moral association of men is in the end directed to the advancement of all in general and of each single member in particular; for they are persons. And thus - to return to Our theme - as the Son of the Eternal Father came down from heaven for the salvation of us all, He likewise established the body of the Church and enriched it with the divine Spirit to ensure that immortal souls should attain eternal happiness according tot he words of the Apostle: "All things are yours; and you are Christ's; and Christ is God's." For the Church exists both for the good of the faithful and for the glory of God and of Jesus Christ whom He sent.
Source: Mystici Corporis Christi (Vatican.va)