Albert Barnes on 1 John 5:1

Whosoever believeth that Jesus is the Christ. Is the Messiah; the anointed of God. On the meaning of the word Christ, Mt 1:1. Of course it is meant here that the proposition, that "Jesus is the Christ," should be believed or received in the true and proper sense, in order to furnish evidence that any one is born of God. Comp. 1Jn 4:3. It cannot be supposed that a mere intellectual acknowledgment of the proposition that Jesus is the Messiah is all that is meant, for that is not the proper meaning of the word believe in the Scriptures. That word, in its just sense, implies that the truth which is believed should make its fair and legitimate impression on the mind, or that we should feel and act as if it were true. Mk 16:16. If, in the proper sense of the phrase, a man does believe that Jesus is the Christ, receiving him as he is revealed as the Anointed of God, and a Saviour, it is undoubtedly true that that constitutes him a Christian, for that is what is required of a man in order that he may be saved. Acts 8:37. Is born of God. Or rather, "is begotten of God." Jn 3:3. And every one that loveth him that begat. That loves that God who has thus begotten those whom he has received as his children, and to whom he sustains the endearing relation of Father. Loveth him also that is begotten of him. That is, he will love all the true children of God; all Christians. 1Jn 4:20. The general idea is, that as all Christians are the children of the same Father; as they constitute one family; as they all bear the same image; as they share his favour alike; as they are under the same obligation of gratitude to him, and are bound to promote the same common cause, and are to dwell together in the same home for ever, they should therefore love one another. As all the children in a family love their common father, so it should be in the great family of which God is the Head.

(a) "Whosoever believeth" Jn 1:12,13