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ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Union
Introduce the Axiom of Union
sqxpexg
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Metamath Proof Explorer
Ascii
Unicode
Theorem
sqxpexg
Description:
The Cartesian square of a set is a set.
(Contributed by
AV
, 13-Jan-2020)
Ref
Expression
Assertion
sqxpexg
⊢
A
∈
V
→
A
×
A
∈
V
Proof
Step
Hyp
Ref
Expression
1
xpexg
⊢
A
∈
V
∧
A
∈
V
→
A
×
A
∈
V
2
1
anidms
⊢
A
∈
V
→
A
×
A
∈
V