"Chapter 30—Enmity Between Man and Satan “I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel.” Genesis 3:15 . The divine sentence pronounced against Satan after the fall of man was also a prophecy, embracing all the ages to the close of time and foreshadowing the great conflict to engage all the races of men who should live upon the earth. GC 505"
"And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel."
Ellen White directly references Genesis 3:15 in this passage.
"God declares: “I will put enmity.” This enmity is not naturally entertained. When man transgressed the divine law, his nature became evil, and he was in harmony, and not at variance, with Satan. There exists naturally no enmity between sinful man and the originator of sin. Both became evil through apostasy. The apostate is never at rest, except as he obtains sympathy and support by inducing others to follow his example. For this reason fallen angels and wicked men unite in desperate companionship. Had not God specially interposed, Satan and man would have entered into an alliance against Heaven; and instead of cherishing enmity against Satan, the whole human family would have been united in opposition to God. GC 505.2"
"And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel."
The EGW passage directly quotes and elaborates on Genesis 3:15, explaining the nature and implications of the enmity God places between Satan and humanity.
"Satan tempted man to sin, as he had caused angels to rebel, that he might thus secure co-operation in his warfare against Heaven. There was no dissension between himself and the fallen angels as regards their hatred of Christ; while on all other points there was discord, they were firmly united in opposing the authority of the Ruler of the universe. But when Satan heard the declaration that enmity should exist between himself and the woman, and between his seed and her seed, he knew that his efforts to deprave human nature would be interrupted; that by some means man was to be enabled to resist his power. GC 505.3"
"And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel."
This EGW passage continues the direct reference to and explanation of Genesis 3:15, focusing on Satan's understanding of the prophecy and its impact on his plans.