Exercise 4, § 4

Tag 03GH, permanent. Cite it as [Bourbaki, Tag 03GH].

Theory of Sets, I, 58

Let $A$ and $B$ be relations in $\mathscr{T}$ and let $x$ be a letter. Show that the relations

(\forall x)(A \text{ or } B) \Rightarrow ((\forall x)A \text{ or } (\exists x)B),

(\exists x)A \text{ and } (\forall x)B \Rightarrow (\exists x)(A \text{ and } B)

are theorems in

\mathscr{T}

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