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Quantifier Consequences

For every formula A and B, the following conclusions hold:

Universal Quantification and Conjunction

(forall x: A /\  B)

(forall x: A) /\  (forall x: B)

(forall x: A) /\  (forall x: B)

(forall x: A /\  B)

Existential Quantification and Disjunction

(exists x: A \/ B)

(exists x: A) \/ (exists x: B)

(exists x: A) \/ (exists x: B)

(exists x: A \/ B)