Truth-functions are not material functions.

If e.g. an affirmation can be produced by repeated denial, is the denial - in any sense - contained in the affirmation?
Does "~~p" deny "~p", or does it affirm p; or both?

The proposition "~~p" does not treat of denial as an object, but the possibility of denial is already prejudged in affirmation.

And if there was an object called "~", then "~~p" would have to say something other than "p".
For the one proposition would then treat of ~, the other would not.

5.441 This disappearance of the apparent logical constants also occurs if
"~(x).~fx"
says the same as "(x).fx", or "(x).fx . x=a"
the same as "fa".

5.442
If a proposition is given to us then the results of all truth-operations which have it as their basis are given *with* it.