From Institutes 2.16.5 (Battles edn):
Now someone asks, How has Christ abolished sin, banished the separation between us and God, and acquired righteousness to render God favorable and kindly toward us? To this we can in general reply that he has achieved this for us by the whole course of his obedience. This is proved by Paul’s testimony: “As by one man’s disobedience many were made sinners, so by one man’s obedience we are made righteous” [Romans 5:19]. In another passage, to be sure, Paul extends the basis of the pardon that frees us from the curse of the law to the whole life of Christ: “But when the fullness of time came, God sent forth his Son, born of woman, subject to the law, to redeem those who were under the law” [Galatians 4:4-5]. Thus in his very baptism, also, he asserted that he fulfilled a part of righteousness in obediently carrying out his Father’s commandment [Matthew 3:15]. In short, from the time when he took on the form of a servant, he began to pay the price of liberation in order to redeem us.
Yet to define the way of salvation more exactly, Scripture ascribes this as peculiar and proper to Christ’s death. He declares that “he gave his life to redeem many” [Matthew 20:28]. Paul teaches that “Christ died for our sins” [Romans 4:25]. John the Baptist proclaimed that he came “to take away the sins of the world,” for he was “the Lamb of God” [John 1:29]. In another passage Paul teaches that “we are freely justified through the redemption which is in Christ, because he was put forward as a reconciler in his blood” [Romans 3:24-25]. Likewise: “We are …justified by his blood …and reconciled …through his death.” [Romans 5:9-10.] Again: “For our sake he who knew no sin was made sin, so that in him we might become the righteousness of God.” [2 Corinthians 5:21] I shall not pursue all the testimonies, for the list would be endless, and many of them will be referred to in their order. For this reason the so-called “Apostles’ Creed” passes at once in the best order from the birth of Christ to his death and resurrection, wherein the whole of perfect salvation consists. Yet the remainder of the obedience that he manifested in his life is not excluded. Paul embraces it all from beginning to end: “He emptied himself, taking the form of a servant …and
was obedient to the Father unto death, even death on a cross”