party. Id. Because the same analysis applies to Google’s use of Perfect 10’s image, the district court did not err in finding that this factor favored neither party.
Effect of use on the market. The fourth factor is “the effect of the use upon the potential market for or value of the copyrighted work.” 17 U.S.C. § 107(4). In Kelly, we concluded that Arriba’s use of the thumbnail images did not harm the market for the photographer’s full-size images. See Kelly, 336 F.3d at 821–22. We reasoned that because thumbnails were not a substitute for the full-sized images, they did not harm the photographer’s ability to sell or license his full-sized images. Id. The district court here followed Kelly’s reasoning, holding that Google’s use of thumbnails did not hurt Perfect 10’s market for full-size images. See Perfect 10, 416 F.Supp.2d at 850–51. We agree.
Perfect 10 argues that the district court erred because the likelihood of market harm may be presumed if the intended use of an image is for commercial gain. However, this presumption does not arise when a work is transformative because “market substitution is at least less certain, and market harm may not be so readily inferred.” Campbell, 510 U.S. at 591, 114 S.Ct. 1164. As previously discussed, Google’s use of thumbnails for search engine purposes is highly transformative, and so market harm cannot be presumed.
Perfect 10 also has a market for reduced-size images, an issue not considered in Kelly. The district court held that “Google’s use of thumbnails likely does harm the potential market for the downloading of [Perfect 10’s] reduced-size images onto cell phones.” Perfect 10, 416 F.Supp.2d at 851 (emphasis omitted). The district court reasoned that persons who can obtain Perfect 10 images free of charge from Google are less likely to pay for a download, and the availability of Google’s thumbnail images would harm Perfect 10’s market for cell phone downloads. Id. As we discussed above, the district court did not make a finding that Google users have downloaded thumbnail images for cell phone use. This potential harm to Perfect 10’s market remains hypothetical. We conclude that this factor favors neither party.
Having undertaken a case-specific analysis of all four factors, we now weigh these factors together “in light of the purposes of copyright.” Campbell, 510 U.S. at 578, 114 S.Ct. 1164; see also Kelly, 336 F.3d at 818 (“We must balance [the section 107] factors in light of the objectives of copyright law, rather than view them as definitive or determinative tests.”). In this case, Google has put Perfect 10’s thumbnail images (along with millions of other thumbnail images) to a use fundamentally different than the use intended by Perfect 10. In doing so, Google has provided a significant benefit to the public. Weighing this significant transformative use against the unproven use of Google’s thumbnails for cell phone downloads, and considering the other fair use factors, all in light of the purpose of copyright, we conclude that Google’s use of Perfect 10’s thumbnails is a fair use. Because the district court here “found facts sufficient to evaluate each of the statutory factors … [we] need not remand for further factfinding.” Harper & Row, 471 U.S. at 560, 105 S.Ct. 2218 (internal quotation omitted). We conclude that Google is likely to succeed in proving its fair use defense and, accordingly, we vacate the preliminary injunction regarding Google’s use of thumbnail images.
IV
Secondary Liability for Copyright Infringement
We now turn to the district court’s ruling that Google is unlikely to be second-
