Revelation 12:11

they--emphatic in the Greek. "They" in particular. They and they alone. They were the persons who overcame. overcame-- (Rom 8:33-34, Rom 8:37; Rom 16:20). him-- (Jo1 2:14-15). It is the same victory (a peculiarly Johannean phrase) over Satan and the world which the Gospel of John describes in the life of Jesus, his Epistle in the life of each believer, and his Apocalypse in the life of the Church. by, &c.--Greek (dia to haima; accusative, not genitive case, as English Version would require, compare Heb 9:12), "on account of (on the ground of) the blood of the Lamb"; "because of"; on account of and by virtue of its having been shed. Had that blood not been shed, Satan's accusations would have been unanswerable; as it is, that blood meets every charge. SCHOTTGEN mentions the Rabbinical tradition that Satan accuses men all days of the year, except the day of atonement. TITTMANN takes the Greek "dia," as it often means, out of regard to the blood of the Lamb; this was the impelling cause which induced them to undertake the contest for the sake of it; but the view given above is good Greek, and more in accordance with the general sense of Scripture. by the word of their testimony--Greek, "on account of the word of their testimony." On the ground of their faithful testimony, even unto death, they are constituted victors. Their testimony evinced their victory over him by virtue of the blood of the Lamb.

— Jamieson-Fausset-Brown Commentary (public domain)