The variable-prop. p ⊃ tildap is. is not identical with the variable-prop. ~(p . ~p). The corresponding universals would be identical. But the one variable prop. says that out of e.g. p ⊃ q you get a tautology by substituting the variable prop. ~(p . ~p) says shews that out of ~(p . q) you get a tautology by substituting ~p for q, whereas the other does not say shew this.