The Active Obedience of Christ
Christ as Mediator entered the federal relation in which Adam stood in the state of integrity, in order to merit eternal life for the sinner. This constitutes the active obedience of Christ, consisting in all that Christ did to observe the law in its federal aspect, as the condition for obtaining eternal life…. Christ merits more for sinners than the forgiveness of sins. According to Gal. 4:4,5 they are through Christ set free from the law as the condition of life, are adopted to be sons of God, and as sons are also heirs of eternal life, Gal. 4:7. All this is conditioned primarily on the active obedience of Christ. Through Christ the righteousness of faith is substituted for the righteousness of the law, Rom. 10:3,4.
[I]f Christ suffered only the penalty imposed on man, those who shared in the fruits of His work would have been left exactly where Adam was before he fell… still confronted with the task of obtaining eternal life in the way of obedience.
The Bible doesn’t actually teach Christ kept the Law *in our place*. The most popular proof text for this teaching is Romans 5:12ff, but that’s assuming to much as well:
http://catholicnick.blogspot.com/2010/06/greek-expert-daniel-wallace-on-romans.html