1 John 5:13
 I write these things to you who believe in the name of the Son of God, that you may know that you have eternal life. (ESV)
The Apostle John is coming to the conclusion of this letter. He has written this letter to a church that was harassed by false teachers. The false teachers had gone, but the damage was done. People's faith was shaken. John says that he has written these things, meaning the whole letter, to those who have faithfully clung to the truth of Jesus Christ. He wants to encourage them.
Those who belong to Jesus Christ need not fear. The winds of false doctrine will blow. But those who believe in the name of the Son of God have assurance. They belong to the Savior. That faith is not something that can be shaken. God holds on tightly to those who belong to him. He is the author and also the finisher of our faith (Hebrews 12:2).
This letter is written to the faithful believers to assure them of the eternal life they have in Jesus Christ. Let's just pause for a moment and consider that term eternal life. We know that after physical death believers in Christ look forward to an eternal life in heaven where death and mourning are forever gone. Yet that is not the only meaning of eternal life.
 And this is eternal life, that they know you, the only true God, and Jesus Christ whom you have sent. (ESV)
Eternal life is knowing God. The very relationship that we have with God is eternal life. He is living in us and is always with us. The eternal one who spoke the world into existence is with you every moment. This is why you need not fear. False teachers can bring confusion, but they cannot take away the eternal life that is in you.
If you are struggling with doubt and have been harassed by the lies of the enemy spend time in the truth of God's Word. Be encouraged! If you believe in the Son of God you have eternal life!