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Quantifier Consequences (Continued)

De Morgan Laws

~forall x: A

exists x: ~A

exists x: ~A

~forall x: A

~exists x: A

forall x: ~A

forall x: ~A

~exists x: A

Such Quantifier

exists x: A

A[x <- such x: A]

(forall y_0, y_1: (A[x <- y_0] /\  A[x <- y_1]) => y_0 = y_1)

(forall x: A => x = such x: A)