A.T. Robertson Commentary 1 John 5:10

"He that believeth on the Son of God hath the witness in him: he that believeth not God hath made him a liar; because he hath not believed in the witness that God hath borne concerning his Son." — 1 John 5:10 (ASV)

Believeth on (πιστευων εις). John draws a distinction between "not believing God" (μη πιστευων τω θεω) in next clause, the testimony of God about his Son, and surrender to and reliance on the Son as here (εις and the accusative). See the same distinction less clearly drawn in Joh 6:30f. See also εις την μαρτυριαν after πεπιστευκεν in this same verse and Joh 2:23.

In him (εν αυτω). "In himself," though the evidence is not decisive between αυτω and αυτω.

Hath made (πεποιηκεν). Perfect active indicative of ποιεω like μεμαρτυρηκεν and πεπιστευκεν, permanent state.

A liar (ψευστην). As in 1:10, which see.

Because he hath not believed (οτ ου πεπιστευκεν). Actual negative reason with negative ου, not the subjective reason as in Joh 3:18, where we have οτ μη πεπιστευκεν). The subjective negative is regular with ο μη πιστευων. Relative clause here repeats close of verse 9.