How do we know Jesus' death was for the elect?

The gospel's narrative affirms that Jesus intentionally laid down His life for the elect, as detailed in John 10:14-15, where He identifies Himself as the Good Shepherd for His sheep. This indicates a clear distinction between all of humanity and those whom God has predestined for salvation. Moreover, in Isaiah 53, the text outlines how the Servant would be stricken for the transgressions of God's people, further emphasizing a precise purpose behind His suffering and death. In the Reformed tradition, it is crucial to uphold that the efficacy of Christ's blood is grounded in God's sovereign choice, ensuring that none of those for whom Christ died will be lost (Philippians 1:6).