Isaiah repeatedly presents YHWH's foretelling of events as evidence of his unique identity.
Isaiah 41:4; Isaiah 43:10; Isaiah 46:9-10 are significant backgrounds.
Jesus' wording closely resembles Isaiah's pattern: prediction is given so that hearers may later know and believe the identity expressed by ego eimi.
The correspondence contributes strongly to John's cumulative divine-name theme, while the phrase itself is not treated mechanically as proof.