Are there any examples of deductive arguments used to defend a doctrine? Does anyone know an example of a doctrine, from any denomination, that is defended via a deductive argument, where the doctrine is logically deduced from an initial set of premises? If so, what about the argument's validity? What about its soundness?

As a reminder of what a deductive argument looks like, the following is an example taken from the Wikipedia article:


All men are mortal. (First premise)
Socrates is a man. (Second premise)
Therefore, Socrates is mortal. (Conclusion)


Another illustrative example of a deductive argument is The Kalam Cosmological Argument:


Whatever begins to exist has a cause of its beginning.
The universe began to exist.
Therefore, the universe has a cause of its beginning.
I'll give the following &quot;syllogism&quot; to deduce the Trinity doctrine. But first I will define what is a syllogism? A syllogism in logic is a form of reasoning in which a conclusion is drawn from two given premises, one major premise and minor premise.
Here is a complex syllogism that &quot;deduces&quot; the Trinity.
If the Bible teaches that there is one God
and
If in the Bible The Father is identified as God
and
If in the Bible His Son is identified as God
and
If in the Bible their Spirit is identified as God
THEN the doctrine of the Trinity is valid
OR
The Bible is wrong.
So what is the definition of the Trinity? The doctrine of the trinity is not an &quot;assumption.&quot; It is the normative systematic theology of God in Christianity and is BASED on the fact that the Bible is explicit in telling us that there is, was and forever will be only ONE God and the fact that the Bible &quot;identifies three (and only three) persons as God.
So by what means does the Bible identify this ONE God?

His names
His titles
His unique attributes
His unique actions
His worship

I am not aware of any other literary, contextual means by which the Bible clearly identifies God. I could be wrong, but I think this list is comprehensive.
I will give two examples of of how this works. For example &quot;His names.&quot; Called by the NAMES of God, (YHWH and its variants) either directly or indirectly, usually both.
Recognized with the TITLES of God, (Lord, king, savior, Alpha and Omega, first and last etc.) I think you get the idea. Enjoy!