How do we know Jesus' death was a penal substitution?

The doctrine of penal substitution is rooted in the recognition that Jesus died not for His own sins, but for the sins of those who would believe in Him. As highlighted in Psalm 22 and other passages, Jesus endured a death that was a direct consequence of sin—both His own in the sense of bearing the sins of others and the break in fellowship with God as He faced the divine wrath due to humanity's transgressions. This is further affirmed in Isaiah 53, where it states that 'the Lord has laid on Him the iniquity of us all.' Scriptural references emphasize that Jesus' death was a substitutionary atonement, fulfilling both the requirement of justice and the means of salvation for those elected in Him.