The Pledge of Future Glory: The Eucharist, Salvation, and Resurrection

What’s the connection between the Real Presence of Christ in the Eucharist, and our own salvation and bodily resurrection? In particular, why does the Catechism call the Eucharist “a pledge of the life to come,” and “an anticipation of the heavenly glory” (CCC 1402)? What did early Church Fathers like St. Irenaeus, St. Augustine, and St. Gregory of Nyssa have to say on this topic? And how does all of this help us to make sense of Jesus’ claim that “I am the living bread which came down from heaven; if any one eats of this bread, he will live for ever; and the bread which I shall give for the life of the world is my flesh” (John 6:51)?