But it is a statement regarding my belief. By removing the "belief" aspect of it, you are changing what the statement says.
You had it right here:
My opinion doesn't enter into it.
It is regardless whether you "believe" the statements or not. They are still truisms.
Look:
If it is dark then it will also be black.
I believe that that if it is dark then it will also be black.
A cat has four legs unless it has more or less than four, in which case it does not have four legs.
I believe that a cat has four legs unless it has more or less than four, in which case it does not have four legs.