And all I'm saying is that what you think is based on an assumption, which I've just explained. And which Matt went over
It is a valid proposition, but is it a necessary truth?
I'll give you an example to explain where I am getting at.
"There is no greatest even number."
Some mathematicians would call the proposition "There is no greatest even number" as a necessarily true statement, and some don't, and would rather describe it in terms of validity. For them, rather than necessarily true, they would call it "proven"- which simply means logically validated by the rules of the mathematical system.
Then one must ask is it a metaphysically necessary truth?