Middle Eastern and Pharaonic religions have mostly bequeathed to humanity the idea that eternal life is a reward from God to good people. On the other hand, eternal torment is God’s punishment for the wicked people, which will happen after the Day of Resurrection. This belief was expressed by Martha, Lazarus’ sister, who Christ raised from the dead, when she was speaking to Christ. In the Gospel of John, chapter eleven, verse twenty-five, Jesus corrected this concept with a new definition when He said to Martha, “I am the resurrection and the life. He who believes in Me, though he may die, he shall live.” So eternal life is the participation in God’s life through Jesus Christ.
As for the second part of your question, what is the proof of the existence of the eternal life, that is, man’s participation in the life of Christ? Participation in the life of Christ bears fruits and produces a life of love, holiness, and joy in the lives of true believers. Also, some of them fulfill the revelation of Christ’s works, such as the authority over demons and releasing people from their bondages, healing the sick, and all the rest of the gifts of the Holy Spirit.