The logic itself doesn't fail.
But the conclusion wouldn't necessarily be true if any of the individual statements aren't true.
In particular, there is no obvious support for the truth of this statement:
- Jesus declares his God to be the God of Abraham, Isaac, and Jacob.
Consider what Jesus himself said:
… Nor does anyone know the Father except the Son, and the one to whom the Son wills to reveal Him.
— Matthew 11:27
No one has seen God at any time. The only begotten Son, who is in the bosom of the Father, He has declared Him.
— John 1:18
But the hour is coming, and now is, when the true worshipers will worship the Father …
— John 1:18
If you had known Me, you would have known My Father also; and from now on you know Him and have seen Him.
— John 14:7
O righteous Father! The world has not known You, but I have known You; and these have known that You sent Me. And I have declared to them Your name, and will declare it, that the love with which You loved Me may be in them, and I in them.
— John 17:25,26
Jesus says that:
- No one has known the Father.
- No one has seen the Father.
- No one has worshipped the Father.
It wasn't until Jesus revealed him to mankind that anyone ever knew of the Father's existence.
This clearly indicates that the Father wasn't the God of Abraham, Isaac, and Jacob, so without evidence to support it, point 3 cannot be considered true.
(One might even make a similar argument for point 1, but one false statement is enough to invalidate the conclusion given in the question.)