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... to have come down from heaven.
John 6:2 & 58 recount Jesus' claim to be the "bread of life". That is, just as we cannot continue living physically without food, so we cannot live spiritually or eternally without the food from heaven - Jesus Himself.

Jesus said to them, " I am the bread of life; he who comes to Me shall not hunger, and he who believes in Me shall never thirst. But I said to you, that you have seen Me, and yet do not believe. All that the Father gives Me shall come to Me, and the one who comes to Me I will certainly not cast out. For I have come down from heaven, not to do My own will, but the will of Him who sent Me." (John 6:3~38)

Who but God alone would dare to make such a claim (Who but God alone, is the source of eternal life?) And yet Jesus claims to be the giver of it.

... to be the source of spiritual fulfillment, the giver of life.
Who can truly satisfy spiritual hunger but God alone?

Now on the last day, the great day of the feast, Jesus stood and cried out, saying, "If any man is thirsty, let him come to Me and drink. He who believes in Me as the Scripture said, 'From his innermost being shall flow rivers of living water."' (John 7:37,38)

Are you empty inside, attempting to fill your life with all kinds of things, and yet never truly satisfied? Come to the Lord Jesus Christ and ask Him for eternal life. He alone is the giver of the "living water" you are so thirsty for. Jesus goes on to say...

"I am the light of the world, he who follows Me shall not walk in the darkness, but shall have the light of life."

Again, Jesus tells people that if they follow Him" they "shall have the light of life." And He claims that God the Father backs Him up regarding His claims in John 8:18 (see also John 9:5 & John 12:46)