It seems obvious enough that, after witnessing the resurrection of Christ, the earliest Christians began to find a great number of parallels in their scriptures (namely, the Old Testament) to the experiences of Jesus himself. They saw that Christ's life in some way fulfilled the things discussed, mentioned, and predicted in the Law and the Prophets. In light of this, we can read the Old Testament as in some way offering an insight into the mind of Christ himself, who certainly would have interpreted his own experiences in its light.
Consider these wonderful verses from Ps 118:
I shall not die, but I shall live,
and recount the deeds of the Lord.
The Lord has punished me severely,
but he did not give me over to death.
Open to me the gates of righteousness,
that I may enter through them,
and give thanks to the Lord.
This is the gate of the Lord;
the righteous shall enter through it.
I thank you that you have answered me,
and have become my salvation (vv. 17-21).
This is the mentality of Christ, who has overcome the world and every obstacle which was set in his way. Conquering temptations and opposition on the part of the religious leaders of Israel, and even suffering the pangs of death on behalf of the whole world, at the resurrection he experiences joy and thankfulness for God the Father's unending love towards him. He provides for us a model for Christian life: unconditional trust in God, even in the face of pains and suffering and death itself.
These verses describe the "salvation" of Christ, or better said, they express the sentiments which Christ felt in his human nature throughout his life and especially after his resurrection. But they also speak to us, who have come to know God's love and mercy for all and each in the good news about Jesus. What else can you say, knowing that your many sins are forgiven you, except this: I thank you ... that you have become my salvation?
Christ could not keep quiet but showed himself to his apostles after his resurrection. Neither could they keep quiet about so great a revelation, for they soon after began to pray and to preach the gospel to all who would hear them. So also neither can you and I keep quiet, if we have truly come to know about the forgiveness of our sins and our restoration to friendship with God. Such a tremendous and expected gift is worth sharing with others! As the psalmist said: I shall not die, but I shall live, and recount the deeds of the Lord. That is what a grateful heart does!