Excerpt from "On The Trinity" treatise by Saint Hilary

We believe that the Word became flesh and that we receive his flesh in the Lord's Supper. How then can we fail to believe that he really dwells within us? When he became man, he actually clothed himself in our flesh, uniting it to himself for ever. In the sacrament of his body he actually gives us his own flesh, which he has united to his divinity. This is why we are all one, because the Father is in Christ, and Christ is in us. He is in us through his flesh and we are in him. With him we form a unity which is in God.

The manner of our indwelling in him through the sacrament of his body and blood is evident from the Lord's own words: This world will see me no longer but you shall see me. Because I live you shall live also, for I am in my Father, you are in me, and I am in you. If it had been a question of a mere unity of will, why should he have given us this explanation of the steps by which it is acheived? He is in the Father by reason of his divine nature, we are in him by reason of his human birth, and he is in us through the mystery of the sacraments. This, surely, is what he wished us to believe; this is how he wanted us to understand the perfect unity that is achieved through our Mediator, who lives in the Father while we live in him, and who, while living in the Father, lives also in us. This is how we attain to unity with the Father. Christ is in very truth in the Father by his eternal generation; we are in very truth in Christ, and he likewise is in us.

Christ himself bore witness to the reality of this unity when he said: He who eats my flesh and drinks my blood lives in me and I in him. No one will be in Christ unless Christ himself has been in him; Christ will take to himself only the flesh of those who have received his flesh.

He has already explained the mystery of this perfect unity when he said: As the living Father sent me and I draw life from the Father, so he who eats my flesh will draw life from me. We draw life from his flesh just as he draws life from the Father. Such comparisons aid our understanding, since we can grasp a point more easily when we have an analogy. And the point is that Christ is the wellspring of our life. Since we who are in the flesh have Christ dwelling in us through his flesh, we shall draw life from him in the same way as he draws life from the Father.

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Saint Hillary was born at Poiters at the beginning of the fourth century. About the year 350 he was chosen bishop of that city, and for his vigorous fight against the Arians was exiled by the Emporer Constantine. To strengthen the Catholic faith and interpret sacred Scripture, he wrote works of wisdom and learning. Saint Hillary died in 367.

From: The liturgy of the hours according to the Roman Rite