"Christianity has always said that the devil is a fallen angel"
Public Domain"I beheld Satan as lightning fall from heaven." Gustave Doré illustration for Paradise Lost, 1866.

Both the Old and New Testaments make references to Satan as a fallen angel. (Quotations below are from the King James Version.)

Isaiah 14:12-15: "How art thou fallen from heaven, O Lucifer, son of the morning! how art thou cut down to the ground, which didst weaken the nations! For thou hast said in thine heart, I will ascend into heaven, I will exalt my throne above the stars of God: I will sit also upon the mount of the congregation, in the sides of the north: I will ascend above the heights of the clouds; I will be like the most High. Yet thou shalt be brought down to hell, to the sides of the pit." ("In the midst of a world of light and love, of song and feast and dance, [Lucifer] could find nothing to think of more interesting than his own prestige." C. S. Lewis, A Preface to Paradise Lost)

Luke 10:18: "And he [Jesus] said unto them, I beheld Satan as lightning fall from heaven."

Cf. Ezekiel 28:11-19; 2 Peter 2:4; Jude 6; Revelation 12.