But an objection is brought, that the flesh of Christ cannot give life, because it was liable to death, and because even now it is not immortal in itself; and next, that it does not at all belong to the nature of flesh to quicken [make alive] souls. I reply, though this power comes from another source than from the flesh, still this is no reason why the designation may not accurately apply to it; for as the eternal Word of God is the fountain of life, (John 1:4,) so his flesh, as a channel, conveys to us that life which dwells intrinsically, as we say, in his Divinity. And in this sense it is called life-giving, because it conveys to us that life which it borrows for us from another quarter. This will not be difficult to understand, if we consider what is the cause of life, namely, righteousness. And though righteousness flows from God alone, still we shall not attain the full manifestation of it any where else than in the flesh of Christ; for in it was accomplished the redemption of man, in it a sacrifice was offered to atone for sins, and an obedience yielded to God, to reconcile him to us; it was also filled with the sanctification of the Spirit, and at length, having vanquished death, it was received into the heavenly glory. It follows, therefore that all the parts of life have been placed in it, that no man may have reason to complain that he is deprived of life, as if it were placed in concealment, or at a distance.
Here is a quote from John Calvin’s commentary on John 6:51. I have bolded that portion that I really enjoyed.