How do we know that Christ's death was a substitutionary atonement?

The concept of substitutionary atonement is pivotal in understanding Christ's redemptive work. In Galatians 3:13, it is stated that Christ redeemed us from the curse of the law by being made a curse for us. This reflects the principle that Christ took upon Himself the penalty that was due for the sins of His people. The priestly work of Christ is not only about intercession but also about His actual sacrificial death on behalf of a particular people – His elect. By examining Romans 8:34, we see that His death and resurrection are unified in purpose; He died for His people and continually intercedes for them. Thus, His sacrifice serves as the substitute for the punishment deserved by sinners, ensuring that justice is met and grace bestowed.