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ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Restricted quantification
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Metamath Proof Explorer
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Unicode
Theorem
nfreu1
Description:
The setvar
x
is not free in
E! x e. A ph
.
(Contributed by
NM
, 19-Mar-1997)
Ref
Expression
Assertion
nfreu1
⊢
Ⅎ
x
∃!
x
∈
A
φ
Proof
Step
Hyp
Ref
Expression
1
df-reu
⊢
∃!
x
∈
A
φ
↔
∃!
x
x
∈
A
∧
φ
2
nfeu1
⊢
Ⅎ
x
∃!
x
x
∈
A
∧
φ
3
1
2
nfxfr
⊢
Ⅎ
x
∃!
x
∈
A
φ