Know we (εγνωκαμεν). Perfect active indicative, "we have come to know and still know." See 1. John 2:3 for "hereby" (εν τουτω).

Love (την αγαπην). "The thing called love" (D. Smith).

He for us (εκεινος υπερ ημων). Εκεινος as in 1. John 2:6; 1. John 3:3; 1. John 3:5, υπερ here alone in this Epistle, though common in John's Gospel (1. John 10:11; 1. John 10:15; 1. John 11:50, etc.) and in 3. John 1:7.

Laid down his life (την ψυχην αυτου εθηκεν). First aorist active indicative of τιθημ, the very idiom used by Jesus of himself in John 10:11; John 10:17.

We ought (ημεις οφειλομεν). Emphatic ημεις again. For οφειλω see 1. John 2:6. Of course our laying down our lives for the brethren has no atoning value in our cases as in that of Christ, but is a supreme proof of one's love (John 13:37; John 15:13), as often happens.