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🏠
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Mathematics
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Set Theory
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Axiom of extensionality
Axiom of extensionality
Two sets are equal if and only if they contain the same elements.
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The statement of the theorem
∀
A
∀
B
(
∀
x
(
x
∈
A
⟺
x
∈
B
)
⟹
A
=
B
)
\forall A \forall B (\forall x (x \in A \iff x \in B) \implies A = B)
∀
A
∀
B
(
∀
x
(
x
∈
A
⟺
x
∈
B
)
⟹
A
=
B
)
.