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CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Predicate calculus with equality: Auxiliary axiom schemes (4 schemes)
Axiom scheme ax-11 (Quantifier Commutation)
nfexa2
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Axiom scheme ax-12 (Substitution)
Metamath Proof Explorer
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Theorem
nfexa2
Description:
An inner universal quantifier's variable is bound.
(Contributed by
SN
, 11-Feb-2026)
Ref
Expression
Assertion
nfexa2
⊢
Ⅎ
x
∃
y
∀
x
φ
Proof
Step
Hyp
Ref
Expression
1
hbe1a
⊢
∃
x
∀
x
φ
→
∀
x
φ
2
1
nfexhe
⊢
Ⅎ
x
∃
y
∀
x
φ