Indeed, but you are presuming a very modern notion of "believes in Him". Even the devils believe (James 2:19), and they do not have everlasting life.
Did the Arians "believe in Him"?
Jesus said to His Apostles: "The one who listens to you listens to Me, and the one who rejects you rejects Me". (Luke 10:16) That is how we know that the Arians, while claiming to believe in Jesus, actually rejected Him, for they rejected the Church's teachings.
-A8
I can only assume that since you read the last line of my previous post that you also read the 2nd last line.
In which case your entire post is moot.