This study aims to describe how subjects construct explicit warrant derived from implicit warrant when completing mathematical proof. This research was conducted on seventeen students of mathematics education study programs by providing tests on vector material in elementary linear algebra courses. The test results show that there are four students who can solve the evidentiary questions correctly using warrant, but there is only one student who can be the subject of research. The selection of subjects is based on students' ability to communicate verbally about the thought process carried out in constructing implicit warrant to explicit warrant when conducting proof. Data in this study were obtained from think aloud, tests, and interviews conducted by researchers to subjects. The results showed that the explicit warrant constructed by the subjects was obtained from an implicit warrant based on the thought process carried out. The subject constructs an explicit warrant derived from an implicit warrant through four steps, namely identifying problems,determining warrant, doing algebraic manipulation, and making conclusions. Warrant is a guarantor used to get the correct conclusions from a mathematical proof, thus further research needs to be done related to warrant. [This paper was published in: "AIP Conference Proceedings" v2215, p060005-1-060005-5, 2020. AIP Publishing (ISBN 978-0-7354-1968-1).]