ド・モルガンの法則
¬ ∃ x F ( x ) → ∀ x ¬ F ( x ) {\displaystyle \,\neg \,\exists x\,{\mathfrak {F}}(x)\,\rightarrow \,\forall x\,\neg \,{\mathfrak {F}}(x)}
∀ x ¬ F ( x ) → ¬ ∃ x F ( x ) {\displaystyle \,\forall x\,\neg \,{\mathfrak {F}}(x)\,\rightarrow \,\neg \,\exists x\,{\mathfrak {F}}(x)}
∃ x ¬ F ( x ) → ¬ ∀ x F ( x ) {\displaystyle \,\exists x\,\neg \,{\mathfrak {F}}(x)\,\rightarrow \,\neg \,\forall x\,{\mathfrak {F}}(x)}