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Utility theorems
nfe2
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nfale2
Metamath Proof Explorer
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Theorem
nfe2
Description:
An inner existential quantifier's variable is bound.
(Contributed by
SN
, 11-Feb-2026)
Ref
Expression
Assertion
nfe2
⊢
Ⅎ
x
∃
y
∃
x
φ
Proof
Step
Hyp
Ref
Expression
1
excom
⊢
∃
y
∃
x
φ
↔
∃
x
∃
y
φ
2
nfe1
⊢
Ⅎ
x
∃
x
∃
y
φ
3
1
2
nfxfr
⊢
Ⅎ
x
∃
y
∃
x
φ