Not in those words. The phrase the book puts into circulation is another: if there is no immortality of the soul, there is no virtue, and therefore everything is permitted. And it does not come as Ivan's thesis; it passes from mouth to mouth, always through third parties, until it returns to him.
In the elder's cell, in Book II, it is brought up by Miusov, when he recounts a drawing-room conversation: Ivan had said that there is no natural law that makes man love humanity, and that, once faith in immortality is destroyed, nothing will be immoral, not even cannibalism. Mitya asks whether that is really what Ivan said, and says he will remember it. Soon after, Rakitin sums it up: if there is no immortality of the soul, there is no virtue, so everything is permitted. In Book V, Alyosha asks whether it means sinking into debauchery, whether it is "everything is permitted," and Ivan answers that he does not renounce the formula.
The version with God is in the mouth of Smerdyakov, in Book XI. In explaining why he killed, he says that Ivan taught him that, if there is no infinite God, there is no virtue at all, and one need not even have it. And on the night of the confession, the devil recites Ivan's article about the man-god, which ends in "everything is permitted, and that's that."
In other words, Ivan never says it as a program. Said by Ivan as a problem, the phrase becomes, in the mouth of someone who receives it without his torment, a license. That is what the book shows.