How do we know Jesus' authority over Satan is true?

In the Gospels, particularly in passages like John 14:30, Jesus explicitly refers to Satan as 'the prince of this world,' indicating a struggle that would occur. However, He also highlights that Satan 'hath nothing in me,' showcasing that He is supreme over darkness. Throughout His ministry, Jesus demonstrates authority over demons, sickness, and sin, culminating in His victory over death and Satan at the cross and resurrection. This authority is a central tenet of the Christian faith, affirming that through Christ, we are liberated from the power of evil and sin, as stated in Colossians 1:13, where believers are rescued from the kingdom of darkness and brought into the kingdom of God's Son.