Catechism of the Catholic Church

616 It is love "to the end" ⁴⁴⁶ that confers on Christ's sacrifice its value as redemption and reparation, as atonement and satisfaction. He knew and loved us all when he offered his life. ⁴⁴⁷ Now "the love of Christ controls us, because we are convinced that one has died for all; therefore all have died." ⁴⁴⁸ No man, not even the holiest, was ever able to take on himself the sins of all men and offer himself as a sacrifice for all. The existence in Christ of the divine person of the Son, who at once surpasses and embraces all human persons, and constitutes himself as the Head of all mankind, makes possible his redemptive sacrifice for all.

617 The Council of Trent emphasizes the unique character of Christ's sacrifice as "the source of eternal salvation" ⁴⁴⁹ and teaches that "his most holy Passion on the wood of the cross merited justification for us." ⁴⁵⁰ And the Church venerates his cross as she sings: "Hail, O Cross, our only hope." ⁴⁵¹