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🏠
/
Mathematics
/
Set Theory
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Axiom of union
Axiom of union
For any set of sets, the union of all its elements is also a set.
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The statement of the theorem
∀
F
∃
A
∀
Y
∀
x
(
x
∈
Y
∧
Y
∈
F
⟹
x
∈
A
)
\forall \mathcal{F} \exists A \forall Y \forall x (x \in Y \land Y \in \mathcal{F} \implies x \in A)
∀
F
∃
A
∀
Y
∀
x
(
x
∈
Y
∧
Y
∈
F
⟹
x
∈
A
)
.