yes, anti is actually a greek prefix, suggesting in place of, etc.
The term is applied generally in John as seen above. However, the Bible does clearly speak of a last day wicked man in several places.
You already mentioned the little horn of Daniel 7, then there is the Beast power in Revelation 13, and then also later in revelation, And there is the "man of sin" or "man of lawlessness" in Thessalonians:
2Th 2:1 Now concerning the coming of our Lord Jesus Christ and our being gathered together to him, we ask you, brothers,
2Th 2:2 not to be quickly shaken in mind or alarmed, either by a spirit or a spoken word, or a letter seeming to be from us, to the effect that the day of the Lord has come.
2Th 2:3 Let no one deceive you in any way. For that day will not come, unless the rebellion comes first, and the man of lawlessness is revealed, the son of destruction,
2Th 2:4 who opposes and exalts himself against every so-called god or object of worship, so that he takes his seat in the temple of God, proclaiming himself to be God.
2Th 2:5 Do you not remember that when I was still with you I told you these things?
2Th 2:6 And you know what is restraining him now so that he may be revealed in his time.
2Th 2:7 For the mystery of lawlessness is already at work. Only he who now restrains it will do so until he is out of the way.
2Th 2:8 And then the lawless one will be revealed, whom the Lord Jesus will kill with the breath of his mouth and bring to nothing by the appearance of his coming.
2Th 2:9 The coming of the lawless one is by the activity of Satan with all power and false signs and wonders,
2Th 2:10 and with all wicked deception for those who are perishing, because they refused to love the truth and so be saved.
2Th 2:11 Therefore God sends them a strong delusion, so that they may believe what is false,
2Th 2:12 in order that all may be condemned who did not believe the truth but had pleasure in unrighteousness.
These are all taken together and referenced by the term "antichrist" though as you note, the term isn't found in those passages save the one in John.