Church Fathers on John 6:35

And Jesus said to them, I am the bread of life. He does not say this of His body, for He speaks of that at the end; The bread that I will give you is My flesh. Here He is speaking of His Divinity. The flesh is bread, by virtue of the Word; this bread is heavenly bread, on account of the Spirit which dwells in it.

He does not say, I am the bread of nourishment, but of life, for, whereas all things brought death, Christ has quickened us by Himself. But the life here, is not our common life, but that which is not cut short by death: He that comes to Me shall never hunger; and, He that believes in Me shall never thirst.

He that comes to Me, i.e. that believes in Me, shall never hunger, has the same meaning as shall never thirst; both signifying that eternal society, where there is no want.