How do we know that Christ's death was for the elect?

In understanding the nature of Christ's atonement, the Bible reveals that His sacrificial death was intentionally for the elect. Passages such as John 10:14-15 affirm that Jesus, as the Good Shepherd, lays down His life for His sheep, indicating a specific and defined group for whom He died. This understanding aligns with the doctrine of limited atonement, where Christ's death effectively secured salvation for those chosen by God rather than merely enabling potential salvation for all. In contrast, Arminianism posits that Christ's atoning work allows every individual the possibility of salvation, a viewpoint that undermines the complete salvation achieved through Christ’s death, which truly satisfies the justice of God only for the elect.