"Steadfast" here is a hebrew word indicating to lay or rest upon. The Christian rests upon the promises of God. He rests upon the atoning work of Christ, and Christ as his mediator. So also we naturally experience peace from such a reliance.
"Peace I leave with you; my peace I give you. I do not give to you as the world gives."Therefore, since we have been justified through faith, we have peace with God through our Lord Jesus Christ." Romans 5:1
Do not let your hearts be troubled and do not be afraid." John 14:27
Our peace of mind is a testimony of our trust in God.