For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
One minor distinction: John 6:51 (KJV) uses the wording; "I am the living bread," as opposed to "the bread of life."
One addition: John 9:5 also says "I am the light of the world."
One small correction: "I am the true vine," should be John 15:5, not John 5.