Jesus' "I am" statements from John's Gospel

Something I've been thinking about:

Of all of Jesus' "I am" statements in John, only one is capitalized, namely where He said "Before Abraham was, I AM" (John 8:58). We know that it hearkens back to Exodus 3, where God spoke to Moses from the burning bush: "I AM who I AM. Thus you shall say to the children of Israel, 'I AM' has sent me to you".

However, I've been wondering: Do Jesus' other "I am" statements in John's Gospel also point back to Exodus 3, even though the "I am" is not capitalized?

Thanks

haYAH asher haYAH

TO be honest it;s not a name, its a derivative of the name YHWH, but here is an explanation of its meaning.

Exodus 3:14, 14 And Elohim said to Mosheh, “I am (H196) that I am (H196). And He said, “Thus you shall say to the children of Yisra’ĕl, ‘I am has sent me to you.”

The Heḇrew text reads: ’eheyeh ’asher ’eheyeh, the word ’eheye hbeing derived from hayah which means to be, to exist.
So eheyeh ’asher ’eheyeh (I am that I am) means I exist that I exist.

H1961 הָיָה hayah (haw-yaw) v.
1. to exist.
2. to be or become.
3. to come into being, i.e. to happen, to occur (always emphatic, and not a mere copula or auxiliary). [a primitive root] Compare: H1933

“יהוה” is word #H3068 יְהוָה Yhvah (yeh-vaw') - יְהוָֹה Yhovah (yeh-ho-vaw') - יְהוֹ Yhow, (yeh-ho') [as a prefix], 1. (meaning) the self-Existent or Eternal, the I AM., 2. (person) Yahweh (Yehvah), Jewish national name of God., 3. (anglicized) Jehovah., 4. (as a name prefix) Yeho-., 5. (As expressed in Hebraic Koine Greek) ἐγώ εἰμί, I AM (literally: I myself, I am)., [from H1961], KJV: Jehovah, the Lord, Root(s): H1961, Compare: H3050, H3069, See also: G1510

I think they refer back to OT titles or positions that the Jewish people would have considered to be God. For example, I am the good Shepherd was no doubt a reference to Psalm 23.

I Am the Bread of Life

I Am the Light of the World

I Am the Gate

I Am the Good Shepherd

I Am the Resurrection and the Life

I Am the Way, the Truth, and the Life

I Am the True Vine

There is also word haVAH H1933 which is the last syllable of His Name and also means to be as well as to breathe.

Transliteration
hāvâ

Part of Speech
verb
Root Word (Etymology)
A primitive root [compare אָוָה (H183), הָיָה (H1961)]
Dictionary Aids
TWOT Reference: 484,491
Variant Spellings
Variant spellings for this word: הוה (Strongs and Gesenius) הוא (Strongs)
KJV Translation Count — Total: 6x
The KJV translates Strong's H1933 in the following manner: be thou (2x), be (1x), shall be (1x), may be (1x), hath (1x).
Outline of Biblical Usage [?]

1. Qal)
   1. to fall
   2. to be, become, exist, happen

Strong’s Definitions [?](Strong’s Definitions Legend)
הָוָא hâvâʼ, haw-vaw'; or
הָוָה hâvâh; a primitive root (compare H183, H1961) supposed to mean properly, to breathe; to be (in the sense of existence):—be, × have.

How is Word spoken. With breath.

I believe that they all should have been capitalized. That would have enabled Christians to see that Exodus 3 is a very powerful testimony to the deity of Christ. Even in the Garden of Gethsemane Christ did not say "I AM he" but "I AM", and it had a huge impact on those who had come to take him prisoner.

.
FAQ: If Jesus didn't exist till Luke 1:26-35, then how could he honestly say:
before Abraham was, I am?

REPLY: The Word per John 1:1-3 became binary when his flesh per John
1:14 was conceived in Mary's womb; thus the Word is quite unique because
he can speak for himself as a material being, and he can speak for himself
as an eternal being, viz: the Word today exists as a divine spirit being and as a
Jewish human being simultaneously.

BTW: Upper upper case spellings in English versions of the New Testament
are oftentimes arbitrary, viz: they're editorial rather than grammatical. A
case in point is John 1:1 wherein theós is typically translated God instead of
god. Caveat Lector.
_

Yes. And when they came to arrest Jesus in the garden of Gethsemane, (John 18), He said, "I am" ("He" is not in the original text) and they fell to the ground. That's how much power there is in that "I am" statement.