A more thorough explanation:

Definition: But-for materiality is a test used in patent law to determine if withheld information would have resulted in the patent being denied. The objective but-for test asks if the patent would have been issued if the applicant had not engaged in misconduct. The subjective but-for test asks if the misrepresentation caused the examiner to issue the patent. The Federal Circuit has rejected the but-for materiality test in favor of the materiality test codified in 37 CFR § 1.56.

Example: If a patent applicant withheld information about prior art that would have made their invention unpatentable, the but-for materiality test would ask if the patent would have been issued if that information had been disclosed. If the answer is no, then the withheld information is considered but-for material.

Explanation: This example illustrates how the but-for materiality test is used to determine if withheld information is important enough to affect the outcome of a patent application. If the information would have resulted in the patent being denied, then it is considered but-for material and the patent may be invalidated.